Write 2, 330, 000 in scientific notation?

At this same time in 2010, 78% of people said they went out dancing at least one night a month. Recently, this number has increa

bezimeni [28]

Answer:

80 %

Step-by-step explanation:

since the percentage has increased by 2%, we say 78%+2%=80%

3 0

3 years ago

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When peanuts are packaged in their shells, most shells have two peanuts inside, but some have three and some only have one. A qu

Oduvanchick [21]

Answer:

H0: p = 0.1 and Ha: p > 0.1

Step-by-step explanation:

At the null hypothesis, we test if the mean or proportion is equal to a certain value.

At the alternate hypothesis, we test if the mean or proportion is less than, more than, or different of the value tested at the null hypothesis.

A quality control inspector wants to determine if more than 10% of all shells contain just one peanut.

The value of 10% = 0.1 is tested, which means that the null hypothesis is $H_{0}: p = 0.1$

Test if it is more than 10% = 0.1, so the alternate hypothesis is: $H_{a}: p > 0.1$

4 0

4 years ago

Find the x-coordinates where f '(x) = 0 for f(x) = 2x + sin(2x) in the interval [0, 2π]. so far I found f'(x)=2cos(2x)+2 cos(2x)

rusak2 [61]

From there, you simply need algebra and a calculator that works in radians.

Take the inverse cos of both sides to get 2x = arccos(-1)

Then divide both sides by 2 to get x = arccos(-1) / 2

Put that into a calculator and you get π/2. But because your bounds are 0 to 2π, you have to add π your solution to get the solution on the other side of the unit circle, which would be (3π/2).

Now that you have the x value, put (π/2) and (3π/2) into f(x) to get the y coordinate.

f(π/2) = 2(π/2) + sin(2(π/2) = π, which means this solution is just (π/2, π)
f(3π/2 = 2(3π/2) + sin(2(3π/2) = 3π, which means this solution is (3π/2, 3π)

6 0

4 years ago

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Gymnast Clothing manufactures expensive soccer cleats for sale to college bookstores in runs of up to 500. Its cost (in dollars)

Murljashka [212]

The relationship between profit and revenue is:

Profit = Revenue - Total Cost
Since the cost is given as a function, the equation will be substituted as
Profit = Revenue - (3,250 + 5x + 0.1x²)

Now, the revenue is a linear graph because it is the number of pairs multiplied the fixed rate. So, the slope is constant.
Revenue = 110x --> this is the function for revenue
Thus, the equation for profit would be

Profit = 110x - 3,250 - 5x - 0.1x²
P = -0.1x²+105x-3,250 --> this is the function for profit

Now, to find the minimum value of x to make profit, differentiate P with respect to x and equate to 0.

dP/dx = 0 = -0.2x + 105
x = 525

Thus, the Gymnast Clothing should manufacture at least 525 pairs in order to make profit.

7 0

3 years ago

Set up the integral that uses the method of cylindrical shells to find the volume V of the solid obtained by rotating the region

Ganezh [65]

Answer:

first exercise

V = 16 π

second exercise

V= 68π/15

Step-by-step explanation:

Initially, we have to plot the graph x = (y − 5)2 rotating around y = 3 and the limitation x = 4

<em>vide</em> picture 1

The rotation of x = (y − 5)2 intersecting the plane xy results in two graphs, which are represented by the graphs red and blue. The blue is function x = (y − 5)2. The red is the rotated cross section around y=3 of the previous graph. Naturally, the distance of "y" values of the rotated equation is the diameter of the rotation around y=3 and, by consequence, this new red equation is defined by x = (y − 1)2.

Now, we have two equations.

x = (y − 5)2

xm = (y − 1)2 (Rotated graph in red on the figure)

The volume limited by the two functions in the 1 → 5 interval on y axis represents a volume which has to be excluded from the volume of the 5 → 7 on y axis interval integration.

Having said that, we have two volumes to calculate, the volume to be excluded (Ve) and the volume of the interval 5 → 7 called as V. The difference of V - Ve is equal to the total volume Vt.

(1) Vt = V - Ve

Before start the calculation, we have to take in consideration that the volume of a cylindrical shell is defined by:

$(2) V=\int\limits^{y_{1} }_{y_{2}}{2*pi*y*f(y)} \, dy$

f(y) represents the radius of the infinitesimal cylinder.

Replacing (2) in (1), we have

$V= \int\limits^{5 }_{{3}}{2*pi*y*(y-5)^{2} } \, dy - \int\limits^{7 }_{{5}}{2*pi*y*(y-5)^{2} } \, dy$

V = 16 π

----

Second part

Initially, we have to plot the graph y = x2 and x = y2, the area intersected by both is rotated around y = −7. On the second image you can find the representation.

<em>vide</em> picture 2

As the previous exercise, the exclusion zone volume and the volume to be considered will be defined by the interval from x=0 and y=0, to the intersection of this two equations, when x=1 and y = 1.

The interval integration of equation y = x2 will define the exclusion zone. By the other hand, the same interval on the equation x=y2 will be considered.

Before start the calculation, we have to take in consideration that the volume of a cylindrical shell is defined by:

$(3) V=\int\limits^{x_{1} }_{x_{2}}{2*pi*x*f(x)} \, dx$

Notice that in the equation above, x and y are switched to facilitate the calculation. f(x) is the radius of the infinitesimal cylinder

Having this in mind, the infinitesimal radius of equation (3) is defined by f(x) + radius of the revolution, which is 7. The volume seeked is the volume defined by the y = x2 minus the volume defined by x=y2. As follows:

$V= \int\limits^{1 }_{{0}}{2*pi*x*(\sqrt{x} + 7) } \, dy - \int\limits^{1 }_{{0}}{2*pi*x*(x^{2}+7) } \, dy$

V= 68π/15

6 0

4 years ago