Choose the model for the problem 2/3 ÷ 2 .

Answer:

Step-by-step explanation:

Solving the equation, it is found that it has no solutions, thus, the student is not correct.

The rate of the change of the volume of the pile, in cubic feet per hour, when the circumference of the base is 8x feet, for this case, is 40x²/π³ cubic ft/ hour.

Suppose that a function is defined as;

[tex]y = f(x)[/tex]

Then, suppose that we want to know the instantaneous rate of the change of the function with respect to the change in x, then its instantaneous rate is given as:

[tex]\dfrac{dy}{dx} = \dfrac{d(f(x))}{dx}[/tex]

If a variable z depends on the variable y, which itself depends on the variable x, then we have:

[tex]\dfrac{dz}{dx} = \dfrac{dz}{dy} \times \dfrac{dy}{dx}[/tex]

(assuming all these derivatives exist).

For this case, we're given that:

[tex]V = \dfrac{r^3}{3}[/tex]    (in cubic ft)

Assuming the cross section being circular, expressing radius 'r' in terms of circumference, we get:
[tex]C = 2\pi r\\\\r = \dfrac{C}{2\pi}\\\\V = r^3/3\\\\V = \dfrac{C^3}{24\pi^2} \: \rm ft^3[/tex]

It is given that rate of change of circumference with respect to time is 5.

Thus, symbolically, we get:
[tex]\dfrac{dC}{dt} = 5[/tex]

Finding rate of change of volume with respect to time:

[tex]\dfrac{dV}{dt} = \dfrac{d\left (\dfrac{C^3}{24\pi^2}\right) }{dC} \times \dfrac{dC}{dt} = \dfrac{3C^2}{24\pi^3} \dfrac{dC}{dt} = \dfrac{5C^2}{8\pi ^3} \: \rm ft^3/hour[/tex]

(using chain rule of differenciation).

At C = 8x ft, we get:
[tex]\dfrac{dV}{dt} = \dfrac{5C^2}{8\pi ^3} \: \text{ft}^3\text{/hour}\\\\\dfrac{dV}{dt} |_{C = 8x} = \dfrac{5(8x)^2}{8 \pi^3} = \dfrac{40x^2}{\pi^3} \: \rm ft^3/hour[/tex]

Thus, the rate of the change of the volume of the pile, in cubic feet per hour, when the circumference of the base is 8x feet, for this case, is 40x²/π³ cubic ft/ hour.

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Answer:

6 Mins

Step-by-step explanation:

I like to solve these questions with a equation.

I form the equations with Orginal Amount + FlowingRateX.

Since we have 2, and we want them to be the same they will be equal to eachother.

30+3x=18+5x

12=2x

x=6

The correct statenments are:

The circumference of a circle is the sum of the external part of the circle.

The formula for calculating the area of a circle is expressed as:

A = πr²

The formula for calculating the circumference is given as:

C = 2πr

r is the radius of the circle

If radius is 2 units

A = π(2)² = 4π

C= 2π(2) = 4π

The numerical values of the area and circumference are equal when r = 2.

If radius is 1 units  < 2 units

A = π(1)² = π

C= 2π(1) = 2π

The numerical value of the area is less than the numerical value of the circumference when r less-than 2.

If radius is 3 units  > 2 units

A = π(3)² = 9π

C= 2π(3) = 6π

The numerical value of the area is less than the numerical value of the circumference when r greater-than 2.

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Answer:

ABD

Step-by-step explanation:

Answer: 0.67%/min or 40%/hr

Step-by-step explanation:

In 30minutes It charges 20%, in 1 minute, it will charge 20/30 = 0.6666

In 1hr it will charge 40%, twice the amount it charged in 30minutes (From 35 to 55)

Answer:

D

Step-by-step explanation:

exponential function is: f(x)=b^x

the function represents exponential growth when b>1

A)b=0.84 < 1 this function decay

B) not exponential function

C) not exponential function

D) b=1.06 >1 growth

Answer:

49 un^2

Step-by-step explanation:

We can split the bird feeder into two parts, a rectangle and a triange.

The rectangle would have a base of 7 un and a height of 5 un

So, the area would be 35 un^2

The trianges base would be 7 un, the same as the rectangle, and the height would be 4 un.

So, the area would be 14 un^2

Therefore, the total area of the bird feeder would be 49 un^2

Answer:

____________________________________

[tex] \large{ \tt{ \star \: S \: O \: L \: U \: T \: I \: O \: N : }}[/tex]

[tex] \large{ \boxed{ \tt{♡ \: VOLUME \: = l \: \times b \: \times h}}}[/tex]

[tex] \longrightarrow \: 4 \frac{1}{3} \times 3 \frac{1}{3} \times 4[/tex]

[tex] \longrightarrow \: \frac{13}{3} \times \frac{10}{3} \times 4[/tex]

[tex] \longrightarrow \: \frac{540}{9} [/tex]

[tex] \longrightarrow \tt \: 57 \frac{7}{9} \: ft ^{3} [/tex]

- HappY LearninG ^_________^

Answer: 57 7/9 is the answer

Step-by-step explanation: 4 times 4 1/3 times 3 1/3 is 57 7/9

The volume of the cylindrical tank is the amount of space in it

The volume of the larger tank is 800 gallons

The volume of the small tank is given as:

v = 100

The volume of a cylinder is:

v = πr²h

For the bigger tank, we have:

V = πR²H

The dimensions are twice the smaller tank. This gives

V = π(2r)² * (2h)

Expand

V = 8πr²h

Substitute v = πr²h in V = 8πr²h

V = 8v

Substitute v = 100 in V = 8v

V = 8 * 100

V = 800

Hence, the volume of the larger tank is 800 gallons

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Answer:

C

Step-by-step explanation:

The diagram goes up in increments of 2/8 5 times, which C represents.

Answer:

1. 3(x^2+10x-24)

Step-by-step explanation:

3x^2 +30x-72

so you want to see what each element has in common with the whole equation.  In this case, everything is divisible by 3 so we take out the 3.

3(x^2+10x-24)

Answer:

x = 146°

Step-by-step explanation:

The 34° angle and the angle marked x are same side interior angles. They are supplementary which means the angles should add up to 180°

34 + x = 180

Subtract 34.

x = 146

Answer:

-3 x 10

Step-by-step explanation:

Because there are 10 questions, all wrong taking away 3 points

3d.79480km thats the answer i think

Answer:

10      if the other it is 20

Step-by-step explanation:

she can get 10 foil balloons that cost $3 becasue 30 / 3 = 10 out of 30  if she usees all the money on foil balloons

she can get 20 plain balloons cost that cost $1.50 because 30 / 1.50 = 20 if she usees all the money on plain balloons

Answer:

3 dogs dont get a bone

Step-by-step explanation:

there are 8 dogs and 5 bones if you give one bone to each dog then 3 dogs will remain without one making the answer 3

hope this helped

Answer:

Step-by-step explanation:

Since the largest triangle is right triangle, the vertical segment is the perpendicular bisector of right angle with vertex at the center of circle.

Then we have

Answer:27

Step-by-step explanation: I think :)

Answer:

tanC

Step-by-step explanation:

tanC = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{6}{10}[/tex]

60 bottles required.

For hemispherical bowl:

[tex]\sf volume: \dfrac{2}{3} \pi r^3[/tex]                         [diameter: 30 cm, radius: 15 cm]

[tex]\rightarrow \sf volume: \dfrac{2}{3} \pi (15)^3[/tex]

[tex]\rightarrow \sf volume: 2250\pi \ cm^3[/tex]

For each cylindrical bottles:

[tex]\sf volume: \pi r^2h[/tex]                          ["r" is 2.5 cm, "h" is 6 cm]

[tex]\rightarrow \sf volume: \pi (2.5)^2(6)[/tex]

[tex]\rightarrow \sf volume: 37.5 \pi \ cm^3[/tex]

So number of required bottles:

Answer:

E) quadrilateral

Step-by-step explanation:

Quadrilateral LMNO has 4 sides, but only two seem to parallel each other and that is why it is only a quadrilateral.

Requirements for each shape:

Square = 4 equal sides, 2 pairs of parallel ones, all right angles

Rectangle = 2 sets of equal and parallel sides, all right angles

Rhombus = 4 equal sides, 2 pairs of parallel ones

Parallelogram = 2 pairs of parallel sides

Quadrilateral = 4 sided polygon with 4 corners

Hope this helps!

The new volume after the edges of the box are increased by 1 unit = 266,491 units^3

The volume of a rectangle= l×w×h

The surface area of the box = (side)^2

The sum of the edges of the box = 216 units

If area of the box x^² = 2002

X = √2002

X = 44.7units

But the sum of the edges = 216 units

44.7 + 44.7 + y = 216

make y the subject of formula,

y = 216 - 89.4

y= 126.6 units

Therefore the length, width and height of the rectangular box = 44.7, 44.7 and 126.6 units respectively.

When additional 1 unit is added to each edge it becomes,

44.7 +1 =45.7,

44.7 + 1 = 45.7and

126.6 + 1 = 127.6 units.

Therefore the new volume = 45.7×45.7 × 127.6 = 266,491 units^3.

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Step-by-step explanation:

Answer:

105.53 m

Step-by-step explanation:

Distance covered until 60°

Distance covered until 30°

Distance in interval (d)

The theoretical probability that Chandra will be chosen as one of the science fair participants is 0.8 or 80%.

Theoretical probability of an event is the ratio of number of favourable outcome to the total expected number of outcome of that event.

Five students, Adriana, Ben, Chandra, Diana, and Ernesto, would each like one of the four spots at the regional science fair.

Their names are placed in a hat, and four names are chosen at random to decide who attends the fair.

The total number of ways 4 names can be taken out from 5 names is,

[tex]^5C_4[/tex].

Here one spot needs to be fixed for Chandra. Now the total number of outcome remain 4 and favourable outcome remain 3.

Thus, the number of ways 4 names can be taken out such that it contains the name Chandra is

[tex]^4C_3[/tex].

The theoretical probability that Chandra will be chosen as one of the science fair participants is,

[tex]P=\dfrac{^4C3}{^5C4}\\P=\dfrac{4}{5}\\P=0.8\\P=80\%[/tex]

Thus, the theoretical probability that Chandra will be chosen as one of the science fair participants is 0.8 or 80%.

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Answer:

  9 and 15 inches

Step-by-step explanation:

The unknown lengths can be found by making use of the formula for the area of a trapezoid.

__

Let x represent the shorter base. Then the longer one is (x+6), and the area is ...

  A = 1/2(b1 +b2)h . . . . area of a trapezoid with bases b1, b2, and height h

  72 = 1/2(x +(x+6))(6)

  24 = 2x +6 . . . . . . . . .  simplify, divide by 3

  18 = 2x . . . . . . . . . subtract 6

  9 = x . . . . . . divide by 2

  15 = x+6 . . . . . . the length of the longer base

The bases are 9 inches and 15 inches in length.

Step-by-step explanation:

khan academy

The formulas that give the standard deviation will be given below.

[tex]\sigma = \sqrt{\dfrac{(67 - 70) ^2 + (67 - 70) ^2 + ( 68 - 70) ^2 + ....+ (73 - 70) ^2}{12}}[/tex]

It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in a variation.

The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.

[tex]\rm \sigma = \sqrt{\dfrac{\Sigma (x_i - \mu)^2}{n}}[/tex]

Juana weighed a sample of 12 jumbo eggs. Here are their weights (in grams): 67, 67, 68, 69, 69, 70, 71, 71, 71, 72, 72, 73

The mean is μ =70 grams.

Then the standard deviation is given as,

[tex]\sigma = \sqrt{\dfrac{(67 - 70) ^2 + (67 - 70) ^2 + ( 68 - 70) ^2 + ....+ (73 - 70) ^2}{12}}[/tex]

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