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Write a general formula to describe each variation.

The square of T varies directly with the cube of a and inversely with the square of d; T = 4 when a = 2 and d = 3

T² =  [tex]\frac{18a^3}{d^2}[/tex]

Few things to note:

i. direct variation: When a variable x varies directly with another variable y, we write it in this form;

x ∝ y.

This can then be written as;

x = ky

Where;

k = constant of proportionality variation.

ii. inverse variation: When a variable x varies inversely with another variable y, we write it in this form;

x ∝ [tex]\frac{1}{y}[/tex]

This can then be written as;

x = k([tex]\frac{1}{y}[/tex])

Where;

k = constant of proportionality or variation

iii. combined variation: When a variable x varies directly with variable y and inversely with variable z, we write it in this form;

x ∝ ([tex]\frac{y}{z}[/tex])

This can then be written as;

x = k ([tex]\frac{y}{z}[/tex])

Where;

k = constant of proportionality or variation

From the question;

The square of T varies directly with the cube of a and inversely with the square of d.

Note that

square of T = T²

cube of a = a³

square of d = d²

Therefore, we can write;

T² ∝ [tex]\frac{a^3}{d^2}[/tex]

=> T² =  k ([tex]\frac{a^3}{d^2}[/tex])        -------------------(i)

Since;

T = 4 when a = 2 and d = 3

We can find the constant of proportionality k, by substituting the values of T=4, a = 2 and d = 3 into equation (i) and solve as follows;

(4)² =  k ([tex]\frac{2^3}{3^2}[/tex])

16 =  k ([tex]\frac{8}{9}[/tex])

8k = 16 x 9

8k = 144

k = [tex]\frac{144}{8}[/tex]

k = 18

Now substitute the value of k back into equation (i);

T² =  18 ([tex]\frac{a^3}{d^2}[/tex])

T² =  [tex]\frac{18a^3}{d^2}[/tex]

Therefore, the general formula that describes the variation is;

T² =  [tex]\frac{18a^3}{d^2}[/tex]

Answer:

0 and 1

Step-by-step explanation:

The solutions are the points of intersection, meaning that the x values must meet at those points. x=0 and x=1 meet at those points of intersection.

Answer:

Will take 8hrs.

Step-by-step explanation:

if pipe 1 takes 6 hrs then the 2nd pipe drains it 3x slower

Which means pipe 1 will take 1 hr slower every 3 hrs taken

and will be at ratio 3:2 for when pipe 2 is used

6 + 2 = 8 (hrs)

Will take 8hrs.

9514 1404 393

Answer:

  A)  3.2

Step-by-step explanation:

In this geometry, all of the right triangles are similar. This means side lengths are proportional:

  short side/hypotenuse = x/8 = 8/20

  x = 8×8/20 = 64/20

  x = 3.2

Answer:

I think the answer is option B

Answer:

I think it is (b

Step-by-step explanation:

35 × 2/7 =

2 × 35 / 7 =

2 × 5 × 7 / 7 =

Simplify 7

2 × 5 =

10

Answer:

B is the answer.

Step-by-step explanation:

Answer:

Arc GH = 78°

Step-by-step explanation:

Inscribed angle = m<GIH = 39°

Measure of arc related to inscribed angle = arc GH = ?

Thus:

m<GIH = ½(arc GH) => Inscribed angles theorem

Substitute

39° = ½(arc GH)

Multiply both sides by 2

2*39° = arc GH

78° = arc GH

Arc GH = 78°

9514 1404 393

Answer:

  96

Step-by-step explanation:

In terms of blocks, the box dimensions are ...

  (14 in)/(3.5 in/block) = 4 blocks

  (21 in)/(3.5 in/block) = 6 blocks

Then the volume in terms of blocks is ...

  V = LWH

  V = (4)(4)(6) = 96 . . . . blocks

There are 96 blocks in the set.

Answer:

Hello There!!

Step-by-step explanation:

The answer is that=>Yes It is a rational number.

hope this helps,have a great day!!

~Pinky~

Answer:

Yes.

Step-by-step explanation:

A rational number is any number that can be written as a fraction. These include whole numbers, fractions, decimals that end, and decimals that repeat. Positive and negative do not affect rationality.

Answer:

a) The probability distribution is [tex]f(x) = \frac{1}{8}[/tex]

b) 0.5 = 50% probability that X will take on a value between 21 and 25.

c) 0.25 = 25% probability that X will take on a value of at least 26.

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

[tex]P(X < x) = \frac{a - x}{b - a}[/tex]

The probability of finding a value between c and d is:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

The probability of finding a value above x is:

[tex]P(X > x) = \frac{b - x}{b - a}[/tex]

Uniform distribution over the interval from 20 to 28.

This means that [tex]a = 20, b = 28[/tex]

a. What’s the probability density function?

The probability density function of the uniform distribution is:

[tex]f(x) = \frac{1}{b - a}[/tex]

In this question:

[tex]f(x) = \frac{1}{28 - 20} = \frac{1}{8}[/tex]

b. What’s the probability that X will take on a value between 21 and 25?

[tex]P(21 \leq X \leq 25) = \frac{25 - 21}{28 - 20} = \frac{4}{8} = 0.5[/tex]

0.5 = 50% probability that X will take on a value between 21 and 25.

c. What’s the probability that X will take on a value of at least 26?

[tex]P(X > 26) = \frac{28 - 26}{28 - 20} = \frac{2}{8} = 0.25[/tex]

0.25 = 25% probability that X will take on a value of at least 26.

=========================================================

Explanation:

There are 4 ways to select 3 aces where order doesn't matter. It's basically the same as saying there are 4 ways to leave out one ace.

Then we have 2 slots left to fill. There are (48*47)/2 = 1128 ways to do this where order doesn't matter. The 48 is from the fact there are 52-4 = 48 cards that aren't aces. We step down to 47 after picking the first non-ace card. The 2 in the denominator is to correct for double counting.

We found there were 4 ways to pick the three aces, and 1128 ways to pick the other two non-ace cards. Overall, there are 4*1128 = 4512 ways to pick all five cards where we have exactly 3 aces.

This is out of 52C5 = 2,598,960 ways to select any five cards from a 52 card deck. I'm using the nCr formula which is

[tex]_n C _r = \frac{n!}{r!*(n-r)!}[/tex]

Use n = 52 and r = 5 to get the value mentioned. The exclamation marks indicate factorial.

------------------------------------

To recap, there are

Dividing the two values gets us the final answer

4512/(2,598,960) = 0.001736079047

This value rounds to 0.00174

The probability that exactly 3 of these cards are Aces is 0.004%.

Given that five cards are drawn randomly from a standard deck of 52 cards, to determine the probability that exactly 3 of these cards are Aces the following calculation must be performed:

Therefore, the probability that exactly 3 of these cards are Aces is 0.004%.

Learn more in https://brainly.com/question/821892

Answer:

28

Step-by-step explanation:

it is missing where ?

based on the answer options I guess it is missing between 20 and 36.

if that is true, then the answer is 28.

the difference between 36 and 44 is 8.

the difference between 20 and 36 is 16.

the right answer should cut the interval of 16 into 2 parts (first logical approach to cut it in 2 halves of 8) and be related to the next interval between 36 and 44 (8).

the solution covering both considerations is the middle of the large interval = 20 + 8 = 28.

Answer:

the y-coordinate will be at (0, 2.4)

the x-coordinate will be at (6, 0)

Step-by-step explanation:

y coordinate of the graph is the point where the curve cuts the y axis

According to the graph, the curve cuts the y axis at y = 2.4. Hence the y-coordinate will be at (0, 2.4)

Similarly, the x-coordinate of the graph is the point where the curve cuts the x-axis

According to the graph, the curve cuts the x-axis at x = 6. Hence the x-coordinate will be at (6, 0)

Answer:

Jessica put $4.88 into her savings account.

Step-by-step explanation:

First, you'll add up how kuch she has spent.

7.37 + 3.75 = 11.12

Secondly, you'll subtract 11.12 from 16.

16 - 11.12 = 4.88

Answer:

Step-by-step explanation:

the pidgeon is flying east

Step-by-step explanation:

pool = 1600 sq.cm

1600 sq.sm = 50cm × 32cm

AB = 50cm

the area of the park of A'B' :

50cm×4=200 sq.cm

Answer:

150

Step-by-step explanation:

if there is a positive correlation

when k increases l should also increase

only 150 is an increase in l

Answer:

   12°

Step-by-step explanation:

Sum of interior angles of the triangle is 180°:

   m∠A + m∠B + m∠C = 180°

   3x + 28° + 5x + 52° + 2x - 10° = 180°

   10x + 70° = 180°

   10x = 110°

   x = 11°

Find the measure of angle C:

   m∠C = 2x - 10° = 2(11°) - 10° = 22° - 10° = 12°

Answer:

Step-by-step explanation:

(2x - 10)° + (5x + 52)° + (3x + 28)° = 180°

10x + 70 = 180

x = 11

m∠C = [ 2(11) - 10 ]° = 12°  

Answer:

.6

Step-by-step explanation:

BUA= A+B-A∩B

.5+.3-.2= .6

Answer:

8

Step-by-step explanation:

8 is the correct answer

Answer:

12 2/3

Step-by-step explanation:

Answer:

616

Step-by-step explanation:

A fraction that is equivalent to 38 is 616

Answer:

1496 cubic inches

Step-by-step explanation:

Answer:

0.0594 = 5.94% probability of rain on November 1 and 2, but not on November 3.​

Step-by-step explanation:

Rain on November 1:

0.9 of 0.6(rain on Oct 31).

0.3 of 0.4(not rain on Oct 31).

Rain on November 2:

Considering rain on November 1, 0.9 probability of rain.

Rain on November 3:

Considering rain on November 2, 0.1 probability of rain.

Find the probability of rain on November 1 and 2, but not on November 3.​

Multiplicating the probabilities:

[tex]p = (0.9*0.6+0.3*0.4)*0.9*0.1 = 0.0594[/tex]

0.0594 = 5.94% probability of rain on November 1 and 2, but not on November 3.​