For the inverse variation equation xy = k, what is the constant of variation, k, when x = 7 and y = 3?

Answer:

I' = 197,474.47 cm^3/min

the rate at which water is being pumped into the tank in cubic centimeters per minute is 197,474.47 cm^3/min

Step-by-step explanation:

Given;

Tank radius r = d/2 = 4.5/2 = 2.25 m = 225 cm

height = 11 m

Change in height dh/dt = 16 cm/min

The volume of a conical tank is;

V = (1/3)πr^2 h .....1

The ratio of radius to height for the cone is

r/h = 2.25/11

r = 2.25/11 × h

Substituting into equation 1.

V = (1/3 × (2.25/11)^2)πh^3

the change in volume in tank is

dV/dt = dV/dh . dh/dt

dV/dt = ((2.25/11)^2)πh^2 . dh/dt ....2

And change in volume dV/dt is the aggregate rate at which water is pumped into the tank.

dV/dt = inlet - outlet rate

Let I' represent the rate of water inlet and O' represent the rate of water outlet.

dV/dt = I' - O'

Water outlet O' is given as 8200 cm^3/min

dV/dt = I' - 8200

Substituting into equation 2;

I' - 8200 = ((2.25/11)^2)πh^2 . dh/dt

I' = ((2.25/11)^2)πh^2 . dh/dt + 8200

h = 3.0 m = 300 cm (water height)

Substituting the given values;

I' = ((2.25/11)^2)×π×300^2 × 16 + 8200

I' = 197,474.47 cm^3/min

the rate at which water is being pumped into the tank in cubic centimeters per minute is 197,474.47 cm^3/min

Answer:

-3x^3 + x^2 + 4x +6

Answer is C

Step-by-step explanation:

Answer: -3x^3 + x^2 + 4x +6

Answer is C

Step-by-step explanation:

The expression of (fog)(x) in the simplest form is [tex](fog)(x)=15x[/tex] and this can be determined by using the arithmetic operations.

Given :

[tex]f(x) = 3x\\g(x) = 5x[/tex]

The following steps can be used in order to determine the expression of (fog)(x):

Step 1 - Write the given function.

[tex]f(x) = 3x\\g(x) = 5x[/tex]

Step 2 - Now, replace 'x' by g(x) in order to determine the expression of (fog)(x).

[tex](fog)(x)=3\;g(x)[/tex]

[tex](fog)(x)=3\times 5x[/tex]

Step 3 - Simplify the above expression.

[tex](fog)(x)=15x[/tex]

The expression of (fog)(x) in the simplest form is [tex](fog)(x)=15x[/tex].

For more information, refer to the link given below:

https://brainly.com/question/5245372

Answer:

23

21+25=46 ÷2 =23 what you do is cancel out the numbers and find the middle

The median of the given data set 12,18,21,25,30,43 is, 23

The middle number or piece of data in a collection is known as the median. Three alternative metrics are employed in mathematics to determine the average value for a given group of integers. They are the mode, median, and mean. The measures of central tendency are this trio of measurements.

Median = {(n+1)/2}th term (for odd)

Median = [(n/2)th term + {(n/2)+1}th term]/2 (for even)

Given that,

The data set 12,18,21,25,30,43

By arranging given data set into ascending order,

12, 18, 21, 25, 30, 43

Median = [(n/2)th term + {(n/2)+1}th term]/2   (for even)

Median = (21 + 25)/2

Median = 23

Hence, the median is 23

To know more about median check:

https://brainly.com/question/280604523

#SPJ2

Answer:  4

Step-by-step explanation:

Answer:

lemme think brb

Step-by-step explanation:

Answer:

–50; –6,250; –3,906,250

Step-by-step explanation:

Answer:it would help of you included a photo because the base is measured differently from the triangles

Step-by-step explanation:

Answer:

A = 19.47

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hypotenuse

sin A = 2/6

Take the inverse sin of each side

sin ^-1 ( sin A) = sin ^-1 (2/6)

A =19.47122063

To the nearest hundredth

A = 19.47

Answer:

The volume of Gabe's kitchen is 680 ft^3

Step-by-step explanation:

The volume of the kitchen can be derived by multiplying the floor area of the kitchen by the height.

Volume = floor area × height

Given;

Floor area = 85 ft^2

Height = 8 ft

Substituting the given values into the equation;

Volume = 85 × 8 = 680 ft^3

The volume of Gabe's kitchen is 680 ft^3

Answer:

y = (1/2) x -10

Step-by-step explanation:

Perpendicular lines are lines make right angles. The slopes of perpendicular lines are opposite reciprocals !

2x + y = -7 rewrite in form y=

y = -7 -2x

slope of this line is -2

perpendicular lines are opposite reciprocals so the line p has a slope = 1/2

line p passes through (8, -6) so plug in point into equation of p and get ?

y = 1/2 x +?

-6 =1/2(8) +?

-6 =4 + ? subtract 4 from both sides

-6-4 = ?

-10 = ?

y = (1/2) x -10

Answer:

(x + 5) (x - 7)

Step-by-step explanation:

To factor this trinomial, you must split the middle term (-2x) into two terms that can be added to get -2x, and multiplied to get -35:

[tex]x^2[/tex] - 2x - 35

[tex]x^2[/tex] - 7x + 5x - 35

Group:

([tex]x^2[/tex] - 7x)  (5x - 35)

Take out GCF (Greatest Common Factor):

x(x - 7)  5(x - 7)

(x + 5) (x - 7)

Answer:

$675.00

Step-by-step explanation:

4500 x 0.05 x 3 = 675

Answer:

It reduces the amount of unknowns needed for modeling.

Step-by-step explanation:

Let's first look at the characteristics of poisson distribution.

The Poisson distribution has the following characteristics:

1. It is a discrete distribution.

2. The occurrences in each interval can range from zero to infinity.

3. Each occurrence is very independent of the other occurrences.

4. It helps describes discrete occurrences over an interval.

5. It reduces the amount of constant and unknown needed for modeling an equation.

Answer:

27

Step-by-step explanation:

Because if it is halfway, that means

halfway=1/2

1/2=1/2 of 54

54/2 or 1/2 of 54=27

PLS MARK ME BRAINLIEST I NEED IT PLEASE

The center of the sign will be 27 feet apart from both ends of the bridge.

Given that,
A footbridge has a span of 54 feet. A sign is to be placed exactly halfway across the bridge. How far will the center of the sign be from each end of the bridge is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,

Since the bridge is 54 feet long,
Now at the center of the bridge, a sign is placed,
So the distance of sign from both ends is equal to half of the total length of the bridge. i.e.
= 54 / 2
= 27

Thus, the center of the sign will be 27 feet apart from both ends of the bridge.

Learn more about arithmetic here:

brainly.com/question/14753192

#SPJ2

Answer:

honestly quite a lot

Step-by-step explanation:

any number from 650-699, and also from 700-749

Answer:

range, 700-749

Step-by-step explanation:

Answer:

im so sorry

Step-by-step explanation:

Answer:

(1/3)*(5 1/2) = 1.83333333333 or 1.8

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

25-10/3=3

Answer:

3 movies

Step-by-step explanation:

You can pay for 3 movies because

5*3=15 and you have to pay for the membership which is 10 so

10+15=25

Answer:

Step-by-step explanation:

The formula for calculating the nth term of an arithmetic sequence is given as;

Tn = [tex]a+(n-1)d[/tex]

a is the first term

n is the number of terms

d is the common difference

If  two terms of an arithmetic sequence are a12=70 and a30=124 then;

T12 = a+(12-1)d = 70

T12 = a+11d = 70...(1)

T30 = a+(30-1)d = 124

T30 = a+29d = 124...(2)

Solving equation 1 and 2 simultaneously to get a and d;

Taking the difference of both equation we have;

29d - 11d = 124-70

18d = 54

d = 54/18

d = 3

Substituting d=3 into equation 1 to get the value of 'a' we have;

a+11(3) = 70

a+33=70

a = 70-33

a = 37

To get the explicit rule for the nth term of the sequence, we will use the formula Tn = a+ (n-1)d where a = 37, d =3

Tn = 37+(n-1)3

Tn = 37+3n-3

Tn = 34-3n

This gives the required nth term

Answer:

3/4 , 3

Step-by-step explanation:

Let one number = x

Other = 4x

Sum:

x + 4x = 15/4

5x = 15/4

x = 3/4

Thus the numbers are 3/4 , 3

Answer:

B

Step-by-step explanation:

In the attached file

Answer: D

Step-by-step explanation:

 2x + (2x +4 ) =40

x= 9

2(9) +4 =22

Answer:

B. 20

Step-by-step explanation:

5P2 is equal to 20 using the permutation formula.

The length of a side of the square is 10 cm.

Length is defined as the measurement or extent of something from end to end.

The perimeter of rectangle is obtained using the formula

perimeter = 2(length+width)

Perimeter of square is obtained using the formula

perimeter = 4(length of one side)

Length of rectangle is 13 cm.

Width of rectangle is 7 cm.

Then the perimeter of rectangle is obtained as

perimeter = 2(length+width) = 2(13+7) = 2*20=40

Perimeter of square is

perimeter = 4(length of one side) = 40

Therefore, length of one side is 10 cm.

To learn more about length, use the link given below:

https://brainly.com/question/8552546

#SPJ5

Answer & Step-by-step explanation:

In this problem, we a re given two points. These points are (-4, 3) and (-2, -1). We can use these points and put them into the slope formula.

[tex]Slope=\frac{y2-y1}{x2-x1}[/tex]

Now, plug in the points to their respectful places.

[tex]Slope=\frac{-1-3}{-2-(-4)}[/tex]

[tex]Slope=\frac{-4}{2}[/tex]

[tex]Slope=-2[/tex]

So, your slope of the the line is -2.

Answer:

The correct option is;

D. 30 and 40

Step-by-step explanation:

Here, we have that the rhombus is a quadrilateral with equal and parallel sides hence the length of the diagonals will be

2 × 25×sinθ  and 2 × 25× cosθ

Therefore tanθ = (2 × 25×sinθ)/(2 × 25× cosθ) = (sinθ)/(cosθ)

Therefore, the root of the sum squares of both diagonals = 50

Therefore, we analyze each of the options as follows

For A. we have √(22² + 40²) = 45.65 ≠ 50 therefore these are not the length of diagonals of the rhombus in question

For B. we have √(26² + 36²) = 44.41 ≠ 50 therefore these are not the length of diagonals of the rhombus in question

For C. we have √(26² + 48²) = 55.59 ≠ 50 therefore these are not the length of diagonals of the rhombus in question

For D. we have √(30² + 40²) = 50 therefore these are possible lengths of diagonals of the rhombus in question.

Answer:

4600 tenths as a Fraction

Since 4600 tenths is 4600 over ten, 4600 tenths as a Fraction is 4600/10.

4600 tenths as a Decimal

If you divide 4600 by ten you get 4600 tenths as a decimal which is 460.00.

4600 tenths as a Percent

To get 4600 tenths as a Percent, you multiply the decimal with 100 to get the answer of 46000 percent.

4600 tenths of a dollar

First we divide a dollar into ten parts where each part is 10 cents. Then we multiply 10 cents with 4600 and get 46000 cents or 460 dollars and 0 cents.

Step-by-step explanation:

Hope this helped!

Stay safe!!!

Answer:

Step-by-step explanation:

To answer this, multiply 4600 by 10:  46000.  There are 46000 tenths in 4600.

Answer:

3 mi

Step-by-step explanation:

There are three squares with side a

The area of a square is s^2 where s is the side length

A of the square is a^2

We have three of them so add the areas together

a^2+a^2+a^2 = 3a^2

This is equal to 27

3a^2 = 27

Divide each side by 3

3/3a^2 = 27/3

a^2 = 9

Take the square root of each side

sqrt(a^2) = sqrt(9)

a = 3