How do I write 18,801,310 in expanded form using exponents

Final answer:

The dimensions of the vegetable patch with the least expensive fence are 10 feet by 5 feet.

Explanation:

To find the dimensions of the vegetable patch with the least expensive fence, we can use the formula for the area of a rectangle: length x width = area.

Let's assume the length of the vegetable patch is 'x' and the width is 'y.'

So, xy = 50.

The cost for the east and west sides is $4 per foot, and the cost for the north and south sides is $2 per foot.

Therefore, the cost of fencing the east and west sides would be 4x, and the cost of fencing the north and south sides would be 2y.

For the least expensive fence, we want to minimize the cost, which means minimizing the sum of 4x and 2y.

We can rewrite the equation as:

y = 50/x.

Now substitute the value of y in the cost equation:

cost = 4x + 2(50/x).

To find the minimum cost, we need to find the derivative of the cost equation and set it equal to zero.

Calculating the derivative and solving for x, we find x = √100 = 10.

Therefore, the dimensions of the vegetable patch with the least expensive fence are 10 feet by 5 feet.

Hence, the number of students who listed Instagram as their favorite app is 409

Let x denote the number of students who listed Instagram their favorite app.

Now the number of people who listed Fb as their favorite app is 32 less than two times number of students who have Instagram as their favorite app.

Hence, the equation so obtained is given by:

786 = 2x - 32

i.e. 2x = 818

i.e. x = 409  

                  Hence, the answer is: 409

Answer:

The answer is C. median and mode.

Step-by-step explanation:

First, we have to ensure that the list of the set of data is from least to greatest: 66, 68, 72, 74, 74, 78, 80 .

The mean = (66 + 68 + 72 + 74 + 74 + 78 + 80) ÷ 7 = 512 ÷ 7 = 73.14 . (Note that the mean is not equal to 74.)

The median = middle number when the set of data is listed in order from least to greatest = the fourth number = 74.

The mode = the temperature that occurred the most = 74 .

These results prove that the median and mode best describe what 74 represents in the data set, because they are the same value.

Answer: C

I think its right. Was it for the I ready diagnostic?

35-3 =32

32/2 = 16

there are 16 pear trees and 19 apple trees

The flux of [tex]\vec f(x,y,z)[/tex] across S is given by the surface integral

[tex]\displaystyle \iint_S \vec f(x,y,z) \cdot d\vec s[/tex]

Join to S the disk D of radius 3 in the plane z = 2, for which we have

[tex]x^2+y^2+2=11 \implies x^2+y^2=9=3^2[/tex]

Let S' = S U D (the union of S and D). Since S' is closed, we can use divergence theorem to compute the flux of [tex]\vec f[/tex] through S' :

[tex]\displaystyle \iint_{S'} \vec f \cdot \vec s = \iiint_R \mathrm{div}\vec f \, dV[/tex]

Compute the divergence of [tex]\vec f[/tex] :

[tex]\mathrm{div}\vec f = \dfrac{\partial\left(z\tan^{-1}(y^2)\right)}{\partial x} + \dfrac{\partial\left(z^3\ln(x^2+5)\right)}{\partial y} + \dfrac{\partial(z)}{\partial z} = 1[/tex]

Compute the volume integral by converting to cylindrical coordinates. Take

[tex]\begin{cases}x=r\cos(\theta) \\ y = r\sin(\theta) \\ z = \zeta \\ dV = dx\,dy\,dz = r\,dr\,d\theta\,d\zeta\end{cases}[/tex]

Then the flux of [tex]\vec f[/tex] across S' is

[tex]\displaystyle \iint_{S'} \vec f \cdot \vec s = \int_{-3}^3 \int_{-\sqrt{9-x^2}}^{\sqrt{9-x^2}} \int_2^{11-x^2-y^2} dV = \int_0^{2\pi} \int_0^3 \int_2^{11-r^2} r \, d\zeta \, dr \, d\theta = \frac{81\pi}2[/tex]

To get the flux across S alone, we subtract from this integral the flux of [tex]\vec f[/tex] across D.

Parameterize D by the vector function

[tex]\vec\sigma(\rho,\phi) = \rho \cos(\phi) \, \vec\imath + \rho \sin(\phi) \, \vec\jmath + 2\, \vec k[/tex]

with [tex]0\le\rho\le3[/tex] and [tex]0\le\phi\le2\pi[/tex].

Get the downward-pointing normal vector to D :

[tex]\vec n = \dfrac{\partial\vec\sigma}{\partial\phi} \times \dfrac{\partial\vec\sigma}{\partial \rho} = -\rho\,\vec k[/tex]

Compute the flux across D :

[tex]\displaystyle \iint_D \vec f\cdot d\vec s = \int_0^{2\pi} \int_0^3 \vec f(\vec\sigma) \cdot \vec n \, d\rho\,d\phi = \int_0^{2\pi} \int_0^3 (-2\rho) \, d\rho \, d\phi = -18\pi[/tex]

So the flux of [tex]\vec f[/tex] across S is

[tex]\displaystyle \iint_S \vec f \cdot d \vec s = \frac{81\pi}2 - (-18\pi) = \boxed{\frac{117\pi}2}[/tex]

To find the flux of f across the part of the paraboloid that lies above the plane z = 2 and is oriented upward, we can use the formula for flux and evaluate the integral.

To find the flux of f across the part of the paraboloid that lies above the plane z = 2 and is oriented upward, we can use the formula for flux: flux = ∫∫(f•n)dA. Here, f(x,y,z) = z tan⁻¹(y²)i + z³ ln(x² + 5)j + zk.

The equation of the paraboloid is x² + y² + z = 11. Using these equations, we can set up the double integral and solve for the flux.

After evaluating the integral, we can find the flux of f across the given surface.

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Answer: $108

Step-by-step explanation:

It would cost $288 to cover the larger rectangular garden.

"It is relationship between two numbers that describe how many times one value can contain another. "

"It is an equation in which two ratios are equal."

[tex]A=l\times w[/tex], where 'l' is length of the rectangle and 'w' is width of the rectangle

For given question,

Let 'l' be the length of the rectangle and the 'w' be the width of the rectangle.

The ratio of dimensions of a rectangular garden would be w:l.

mulch is needed to cover a larger, similar garden.

The ratio of dimensions is 2:3

As both the gardens are similar, their dimensions must be in proportion.

[tex]\Rightarrow \frac{w}{2}= \frac{l}{3}[/tex]

[tex]\Rightarrow \frac{w}{l}= \frac{2}{3}[/tex]

So, the length of the larger rectangular garden would be [tex]3l[/tex]

and the length of the larger rectangular garden would be 2w

A mulch to cover the first rectangular garden costs $48.

This means, for the area of [tex]A_1=l\times w[/tex] it costs $48.

Using the formula for area of rectangle the area of the larger garden would be,

[tex]A_2=3l\times 2w\\A_2=6(l\times w)\\A_2=6\times A_1[/tex]

For the second garden it would costs,

6 × 48 = 288

Therefore, it would cost $288 to cover the larger rectangular garden.

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Answer: There would be 56 tubes, 112 packets and 85 toothbrushes in the dental care bags.

Step-by-step explanation:

Since we have given that

Number of tubes of toothpaste = 56

Number of packets of floss = 112

Number of toothbrushes = 85

We need to find the greatest number of identical dental care bags that dentist can make with the least amount of items leftover.

So, we will find "H.C.F." of 56, 112, 85 which is equal to 1.

So, there would be 56 tubes, 112 packets and 85 toothbrushes in the dental care bags.

Answer:

1 pound of granite

Step-by-step explanation:

The density of granite is 168.6 lb/ft³. The volume occupied by 1 pound of granite is:

1 lb × (1 ft³/168.6 lb) = 0.00593 ft³

The density of basalt is 188 lb/ft³. The volume occupied by 1 pound of basalt is:

1 lb × (1 ft³/188 lb) = 0.00532 ft³

As we can see, 1 pound of granite takes up more space than 1 pound of basalt.

Answer:

A. 5825

Step-by-step explanation:

Given: The number of customers for a new online business can be modeled by y = 6x^2 + 75x + 200, where "x" represents the number of months.

We are asked to find number of customers in month 25.

To find the number of customers in 25th month, we need to plug x = 25 in the given function.

y = 6([tex]25)^2[/tex] + 75(25) + 200

y = 6(625) + 1875 + 200

y = 3750 + 1875 + 200

y = 5825

Therefore, the answer is A. 5825

To achieve an annual income of $18,930, the woman should invest $77,700 at the 10% rate and $62,000 at the 18% rate.

To determine how much a woman should invest at each rate to achieve an income of $18,930 per year, we can set up a system of linear equations. Assuming she invests x dollars at the 10% rate and y dollars at the 18% rate, we can use the following equations:

x + y = $139,700: This equation represents the total amount of money she has to invest.

0.10x + 0.18y = $18,930: This equation represents the annual income from the investments.

To solve:

Multiply the first equation by 0.10:

0.10x + 0.10y = $13,970

Subtract this from the second equation:

0.18y - 0.10y = $18,930 - $13,970

0.08y = $4,960

Divide by 0.08 to find y:

y = $62,000

Substitute y back into the first equation to find x:

x + $62,000 = $139,700

x = $77,700

Therefore, the woman should invest $77,700 at the 10% rate and $62,000 at the 18% rate to achieve her desired income.

Answer:

89,349

Step-by-step explanation:

i just did this problem on aleks and this is the answer they gave me how it helps other in the future

Jim would need 5 years to earn interest equal to half of his original principal at a 10% simple interest rate.

To find out how many years it would take for Jim to earn interest equal to half of his original principal at a 10% simple interest rate, we use the formula for simple interest: I = PRT, where I is the interest, P is the principal, R is the rate of interest per year, and T is the time in years.

In this case, Jim wants the interest I to be half of the principal P. So the equation becomes :

[tex]\frac{P}{2} = P \times 0.10 \times T[/tex] or T

=  [tex]\frac{P}{2 \times P \times 0.10}[/tex], which simplifies to T =[tex]\frac{1}{2 \times 0.10}[/tex]or T = 5 years. Therefore, the correct answer is C. 5 years.

Answer:

The integer which represents the submarine's position in feet (depth) after it ascends to avoid the cliff = -664

Step-by-step explanation:

It submerges and dives to −972 feet. Then, it ascends 308 feet.

Initially it goes down by 972 feet and then goes up by 308 ft.

Since depth is more than elevation.

Final position is below sea level.

Final depth = 972 - 308 = 664 ft

The integer which represents the submarine's position in feet (depth) after it ascends to avoid the cliff = -664

Answer: c. g may cause h

Step-by-step explanation:

Correlation: It represents the relation between any two or more than two variable.

Causation: It is a kind of correlation where one variable if affected by the other variable.

Therefore , Causation implies correlation.

But correlation does not imply causation.

Hence, if  there were a strong correlation between the variables g and h, then g may cause h.

Answer:

Plan B

Step-by-step explanation:

Plan B and plan C start out at the same increase: 10% ($0.50) for the first week. The increase under plan C stays at 10% of the original value, but the increase under plan B increases according to the value the week before, which keeps getting larger.

Hence, plan B gets to $8.00 the fastest — after about 5 weeks.

Answer:

Step-by-step explanation:

When dealing with consecutive integers, it often simplifies the problem to work with their average value. We know the average value of the integers in this problem is the even integer between the middle two. We can call it x, and write the equation ...

  (x-3) +(x-1) +(x+1) +(x+3) = -72

This simplifies to ...

  4x = -72 . . . . . . . we knew this before we wrote the above equation, since the sum of 4 numbers is 4 times their average.

  x = -18 . . . . . . . . the middle number of the sequence

So, the numbers are:

_____

A more conventional approach is to define the variable as the integer at one end or the other of the sequence. If we make it be the lowest number, then the equation is ...

  (x) +(x +2) +(x +4) +(x +6) = -72

and that simplifies to ...

  4x +12 = -72 . . . . . collect terms

  4x = -84 . . . . . . . . subtract 12

  x = -21 . . . . . . . . . . divide by 4

Now, the other three numbers are found by adding 2, 4, and 6 to this one.

The coordinates of the x-intercept are (B/C,0)

The x-intercept of a graph is defined as the places where the graph crosses the x-axis or the locations where the coordinate of the y-axis equals 0, which are known as the x-intercept of a graph.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Consider the graph of Cx + Ay = B

Here A, B, and C are all positive constants.

To determine the coordinates of the x-intercept

⇒ Cx + Ay = B,

Substitute the value of y = 0 and solve for x

⇒ Cx + A(0) = B,

⇒ Cx = B,

Divide both sides by C

⇒ x = B/C

Hence, the coordinates of the x-intercept are (B/C,0).

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Answer is provided in the image attached.