W varies inversely as the square of t. If W = 12 when t = 2,

find t when W = 27.

A. 27t = 24

B. 27t2 = 48

C. 108 = 12t

D. 12t = 54

Answers

Answer 1

Answer:

B

Step-by-step explanation:

Given W varies inversely as t² then the equation relating them is

W = [tex]\frac{k}{t^2}[/tex] ← k is the constant of variation

To find k use the condition W = 12 when t = 2, thus

12 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )

k = 48

W = [tex]\frac{48}{t^2}[/tex] ← equation of variation

When W = 27, then

27 = [tex]\frac{48}{t^2}[/tex] ( multiply both sides by t² )

27t² = 48 → B

Answer 2

B)  27 t² = 48 will be the algebraic equation for t if W = 27.

What is proportionality?

In arithmetic, proportional or proportional meaning denotes equivalence between two ratios. In the equation a/b = c/d, a and b have the same percentage as c and d. A percentage is primarily established for solving a word problem using one of its four unknown quantities.

Given W varies inversely proportional to t² then the algebraic equation relating them is

W =  k / t² is the constant of variation

for k we can use the condition W = 12 when t = 2,Hence,

12 =  k / 2²

k = 48

When W = 27, then

27 = 48 / t²  ( multiply by t² )

Therefore, t in the form of algebraic equation is 27 t² = 48 Hence, option B is correct.

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Related Questions

Declan says that for any number n, the product 4x n is greater than 4. Which value of n shows why Declan is incorrect

Answers

Answer:

[tex]n > 1[/tex]

Step-by-step explanation:

Given

Statement: 4x n is greater than 4

Required

Value of n

First we need to rewrite the statement in algebraic form;

Product 4 * n is represented by 4n

greater than 4 is represented by > 4

Bringing these two together, it gives the following

[tex]4n > 4[/tex]

Divide through by 4

[tex]\frac{4n}{4} > \frac{4}{4}[/tex]

[tex]n > 1[/tex]

We've arrive at solution;

This means that n is greater than 1

So, the values of n must start from 2 to show that the condition is true

The value of n = 7/8 makes the inequality 4n > 4 false because 7/8 is less than 1.

What is inequality?

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than, known as inequality.

We have n as a number.

4n > 4

Plug n = 5

20 > 4 (true)

Plug n = 9/5

36/4 > 4

9 > 4 (true)

Plug n = 3

12 > 4 (true)

Plug n = 7/8

28/8 > 4

3.5 > 4  (false)

Thus, the value of n = 7/8 makes the inequality 4n > 4 false because 7/8 is less than 1.

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How to change miles per hour to feet per second?

Answers

Answer:

1 mph = 1.46666667  fps

Can someone explain this step by step

Answers

Answer:

Step-by-step explanation:

[tex]1)\sqrt[4]{81h^{4}}=\sqrt[4]{3*3*3*3*h^{4}}\\\\=\sqrt[4]{3^{4}*h^{4}}\\\\ =3*h\\\\=3h[/tex]

Find def, help geometry

Answers

Answer:

d

Step-by-step explanation:

The amounts of Cathy’s last six clothing purchases were $109, $72, $99, $15, $99, and $89. For each question, choose the mean, median, or mode and give its value.



C.) Which value would Cathy NOT tell her parents to convince them that she needs an increase in her allowance?



{I only need help on part C}

Answers

Answer:

The mean value = $80.5

Step-by-step explanation:

The value of her last six spendings are $109, $72, $99, $15, $99, and $89.

For the mean.

Mean = Total spendings/number

Mean =483/6

Mean = $80.5

For the median.

Lets arrange it in ascending order

$15 ,$72, $89, $99, $99, $109

The middle values are two.

Median = (89+99)/2

Median = 188/2

Median = $94

For the mode

$15 ,$72, $89, $99, $99, $109

Highest occuring is $99 with two frequencies.

To convince her parents that she needs an increase in allowance she would show them the bigger spendings .

So the least value on the list it's mean value which is $80.5.

Solve by completing the square:
x2 + 3x – 9 = 0

Answers

Answer:

Step-by-step explanation:

x = 9/5

The solution of the equation [tex]x^2 + 3x - 9 = 0[/tex] by completing the square would be [tex]x = \pm ( \dfrac{\sqrt{45}}{2} - \dfrac{3}{2} )[/tex].

Used the concept of a quadratic equation that states,

An algebraic equation with the second degree of the variable is called a Quadratic equation.

Given that the equation is,

[tex]x^2 + 3x - 9 = 0[/tex]

Now completing the square as

[tex]x^2 + 3x - 9 = 0[/tex]

Add and subtract by 9/4,

[tex]x^2 + 3x + \dfrac{9}{4} - \dfrac{9}{4} - 9 = 0[/tex]

[tex]x^2 + 3x + ( \dfrac{3}{2})^2 - \dfrac{9}{4} - 9 = 0[/tex]

[tex](x + \dfrac{3}{2} )^2 - ( \dfrac{9}{4}+ 9) = 0[/tex]

[tex](x + \dfrac{3}{2} )^2 - ( \dfrac{45}{4}) = 0[/tex]

[tex](x + \dfrac{3}{2} )^2 = ( \dfrac{45}{4})[/tex]

Taking square root on both sides,

[tex](x + \dfrac{3}{2} ) = \pm ( \dfrac{\sqrt{45}}{2})[/tex]

Therefore, the solution of an equation is,

[tex]x = \pm ( \dfrac{\sqrt{45}}{2} - \dfrac{3}{2} )[/tex]

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SOMEONE HELP PLSSS
suppose your friends parents invest $10,000 in an account paying 5% compounded annually. what will the balance be after 5 years?

Answers

Answer:

12,762.82$

Step-by-step explanation:

10,000(1+0.05)^5

Find the volume of the rectangular prism.







Formula: V = lwh



A.
84 m cubed

C.
72 m cubed

B.
89 m cubed

D.
92 m cubed

Answers

Answer:

84m³ (A) should be correct

Answer:

A

Step-by-step explanation:

Volume = length × width × height

= 7 × 4 × 3

= 84 m²

What is the mean absolute deviation of this data set? 26, 31, 32, and 39

Answers

Answer:

3.5

Step-by-step explanation:

26, 31, 32, and 39

First we need to find the mean

(26+ 31+ 32+ 39) /4

128/4 = 32

The mean absolute deviation is sum of   the positive difference between the number and the mean  divided by the number of terms

((32-26)+ (32-31)+ (32-32)+ (39-32)) /4

14/4

3.5

PLEASE HELP!!

The figure is made up of a rectangle and 2 right triangles.

What is the area of the figure?


O 1259 units2

O 1292 units2

O 1413 units2

O 1566 units2

Answers

The rectangle is 28×34 and the two triangles are (1/2) 11 (28) and (1/2) (9)(34)

A = 28(34) +  (1/2) 11 (28) + (1/2) (9)(34)

A = 1259

Answer: 1259 sq units

Which number sentence is true?
A. 78 = 68
B. 78 < 69
C. 78 = 75
D. 78 < 81
E. 78 > 84​

Answers

Answer: the answer choice “d” is correct

Step-by-step explanation:

because the different symbols mean different things and yeah

Answer:

D

Step-by-step explanation:

lesser value -------    < --------This side bigger value {open mouth}

78 < 81

81 is bigger than 78

How many ways can you plant 15 flowers from a group of 36 flowers?

Answers

Answer:

30.

Step-by-step explanation:

You could do 15 times the amount by 2 then add 6.

Twenty people apply for an open position at an accountant's office. The distribution of ages of the applicants is shown in the box plot.

Distribution of Applicant's Ages

How many of


age in years

the applicants have ages that fall within the box of the box plot?


Please help!!!!

Answers

Answer:

The number of applicants that have ages that fall within the box of the boxplot = 10.

Step-by-step explanation:

box plot is constructed from five values: the minimum value, the first quartile, the median, the third quartile, and the maximum value.

The boxplot usually consists of a box and a whisker plot.

The whiskers represent data that is less than the first quartile or 25th percentile and data that is more than the third quartile or 75th percentile.

The box of the boxplot is bounded by the first quartile or 25th percentile and the third quartile or 75th percentile.

Hence, the fraction of the distribution that is usually contained in the box of the boxplot is (75 - 25), 50% of the distribution.

The total number of applicants = 20

50% of 20 = 10.

Hence, the number of applicants that have ages that fall within the box of the boxplot = 10

Hope this Helps!!!

Jarods bicycle wheel has a diameter of 27 inches. How far will the wheel have traveled in one full rotation? Use 3.14 for pi

Answers

Answer:

84.78 in

Step-by-step explanation:

in order to figure out how long it will travel you will need to find the circumference in order to do that you have to do [tex]2 *\pi * radius[/tex] so that is  [tex]2*3.14*13.5[/tex] which equals 84.78  

What is the surface area of this design?

Answers

Answer:

440 inches squared - the last option

Step-by-step explanation:

Step 1. Surface area of top square.

5 x 5 = 25 inches sq

Step 2. Surface area of the 4 sides of the cuboid.

5 x 8 = 40 inches sq

40 x 4 = 160 inches sq

Step 3. Surface area of the large square.

10 x 10 = 100 inches sq

100 - 25 (because it's being covered) = 75 inches sq

Step 4. Surface area of the 4 sides of the large flat cuboid.

2 x 10 = 20 inches sq

20 x 4 = 80 inches sq

Step 5. (OPTIONAL) Surface area of the bottom

10 x 10 = 100 inches sq

Step 6. Add up all.

25 + 160 + 75 + 80 (+ 100 if including the base) = 340

We can conclude that we have to include the base as well because 340 inches sq is not an option listed.

340 + 100 = 440 inches sq

440 inches sq is the last option

Hope this helps :)

Complete 4 A,B 9 for points.

Answers

Answer:

R = (1/t) (A/P - 1)

T = (1/r) (A/P - 1)

does anyone know this ????

Answers

Answer:

What exactly is the question asking? Is that the full question? The answer is 20

Step-by-step explanation:

Answer:

20 sq units

Step-by-step explanation:

HELP!!!!!!!!!



Plz Show working:)​

Answers

Step-by-step explanation:

Hope this help you !! ;))

answer of (ii) : perimeter = 66m

area = 272m^2

math question screen shot down below

Answers

Answer:

A

Step-by-step explanation:

If the current amount he has is B and its 7 LESS then he had earlier add 7 back to find the amount he add  at the start.

Answer:

b+7,Option 1

Step-by-step explanation:

Let the number of buttons Cole had at first be a,

We know,now he has b buttons remaining which is 7 less than a

In other words,

a-7=b

or,a=b+7

If each quadrilateral below is a rectangle find the missing measure in #5

Answers

Answer:

What do you mean by #5?

Step-by-step explanation:

HELP ASAP 30 POINTS!~!!!


You start with a penny which doubles each day for 30 days. How much money would you have after 30 days?

Answers

I got 536870912 hope this helps

wil give bianleast
What are the first four terms in the multiplication pattern given by the formula: 2 • 4n?


8, 32, 128, 512


8, 32, 64, 512


2, 8, 32, 128,


32, 128, 512, 2048

Answers

Answer: B, but technically, all of them are correct except C.

Step-by-step explanation:

First, you fill in 1 for n:

= 2 x 4(1)

= 2 x 4

= 8

Next, I filled in 4 for n:

= 2 x 4(4)

= 2 x 16

= 32

Then, I filled in 8 for n:

= 2 x 4(8)

= 2 x 32

= 64

You can already figure this one out, and the answer is B.

Answer:

all are correct except the third choice.

What type of function is represented?

Answers

Answer:

b

Step-by-step explanation:

ITS B NOT C ITS B ITS B ITS B.

Which is the graph of g(x) = [X + 3]?

Answers

Answer

D or the fourth one because i took the quiz and got it right

Yehudy invested $19.250 in a simple interest account. After 6 years and no additional deposits or withdrawals, the account balance was
$22.957.55. Find the interest rate for the account. Round to the nearest hundredth of a percent if needed

Answers

Answer: 3.21%

Step-by-step explanation:

Interest = (1/t)(A/P - 1)

49 increased by twice a number m

Answers

Answer:

The third one I think

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

First -> twice m is -> 2m

Then

49 increased so -> 49+2m

Brainliest and 10 points for answer!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

How do you find the x- and y-intercepts of an equation?

A) To find the x-intercept, substitute 0 for x. To find the y-intercept, substitute 0 for x.

B) To find the x-intercept, substitute 0 for x. To find the y-intercept, substitute 0 for y.

C) To find the x-intercept, substitute 0 for y. To find the y-intercept, substitute 0 for x.

D) To find the x-intercept, substitute 0 for y. To find the y-intercept, substitute 0 for y.

Answers

Answer:

To find the x-intercept of a given linear equation, plug in 0 for 'y' and solve for 'x'. To find the y-intercept, plug 0 in for 'x' and solve for 'y'.

Answer:

C

Step-by-step explanation:

A, B, and D don't make sense

What is the value of b? -8/5b = 8

Answers

Answer:

-0.2 or -2/10

Step-by-step explanation:

hope this helps

help me you don’t have to explain!!

Answers

Answer:

option b ................

the choice you should choose is answer b

What is the value of x in the figure? Enter your answer in the box.
HELP IMMEDIATELY!

Answers

Answer:

Step-by-step explanation:

145 = 2x + 15

2x = 130

x = 65 (ANS)

Answer:

65º

Step-by-step explanation:

145º = (2x + 15)º

145º = (2x + 15)º

145º - 15º = 2xº + 15º - 15º

130º = (2x)º

x = 65º

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