Write an inequality and then solve.
9. A freight elevator can safely hold no more
than 2200 pounds. An elevator operator must
take 60-pound boxes to a storage area. If the
operator weighs 155 pounds, how many boxes
can be safely moved at one time?

Answer:

32

Step-by-step explanation:

The given set has 5 elements, meaning it has 2⁵ = 32 subsets.

This means the cardinality of the desired set is 32.

Answer:

Answer:

#1) & #5) are the rates that have the same constant rate of change as Micheal's rate.

Answer:

120

Step-by-step explanation:

l = (w*3)+2

w = 6

area = ((6*3)+2) * 6

            ((18) + 2) * 6

               20        * 6

                     120

Step-by-step explanation:

let the number of wholewheat bread batches be x

let the number of muffin batches be y

prep condition: 4x + (1/2)y ≤ 16 or 8x + y ≤ 32

baking condition : 1x + (1/2)y ≤ 10 or 2x + y ≤ 20

graph each of those in the first quadrant shading in the region below each one.

Final shading is the region satisfying both conditions.

profit = 35x + 10y

allow this line to "slide" away from the origin as far as you can.

It should be clear that the farthest we can go is the intersection of

8x+y = 32 and

2x + y = 20 or the x and y intercepts of our two boundary lines.

subtract them as they are:

6x = 12

x = 2

then in our head , y = 16

max profit = 2(35) + 10(16) = 230

Just to make sure, I will test the intercepts of our intersecting region, namely (4,0) and (0,20)

for (4,0) profit = 4(35)+1 = 140

for (0,32) profit = 0 + 10(20) = 200

so max profit is 230 when x=2 and y=16

(notice all the prep time and baking time is utelized)

Following the first term [tex]n[/tex], the [tex]k[/tex]-th term [tex]\left(k\in\{1,2,3,\ldots,n\}\right)[/tex] in [tex]f(n)[/tex] is given by

[tex]\dfrac{16k + (9-4k)n - 3n^2}{4kn + 3n^2}[/tex]

That is,

[tex]k=1 \implies \dfrac{16 + (9-4)n - 3n^2}{4n + 3n^2} = \dfrac{16 + 5n - 3n^2}{4n + 3n^2}[/tex]

[tex]k=2 \implies \dfrac{16\cdot2 + (9-8)n - 3n^2}{4\cdot2n + 3n^2} = \dfrac{32 + n - 3n^2}{8n + 3n^2}[/tex]

and so on, up to

[tex]k=n \implies \dfrac{16n + (9-4n)n - 3n^2}{4n^2 + 3n^2} = \dfrac{25n - 7n^2}{7n^2}[/tex]

We then have

[tex]\displaystyle f(n) = n + \sum_{k=1}^n \frac{16k + (9-4k)n - 3n^2}{4kn + 3n^2} \\\\ ~~~~~~~ = n + \frac1n \sum_{k=1}^n \frac{16\frac kn + 9}{4\frac kn + 3} - \frac1n \sum_{k=1}^n \frac{4kn + 3n^2}{4k + 3n} \\\\ ~~~~~~~ = n + \frac1n \sum_{k=1}^n \frac{16\frac kn + 9}{4\frac kn + 3}- \frac1n \sum_{k=1}^n n \\\\ ~~~~~~~ = \frac1n \sum_{k=1}^n \frac{16\frac kn + 9}{4\frac kn + 3}[/tex]

Now as [tex]n\to\infty[/tex], the right side converges to a definite integral.

[tex]\displaystyle \lim_{n\to\infty} f(n) = \lim_{n\to\infty} \frac1n \sum_{k=1}^n \frac{16\frac kn + 9}{4\frac kn + 3} \\\\ ~~~~~~~~~~~~~ \,= \int_0^1 \frac{16x + 9}{4x + 3} \, dx[/tex]

Wrap up by substituting [tex]x\mapsto\frac{x-3}4[/tex].

[tex]\displaystyle \lim_{n\to\infty} f(n) = \frac14 \int_0^1 \frac{16x + 9}{4x + 3} \, dx \\\\ ~~~~~~~~~~~~~\, = \frac14 \int_3^7 \frac{4x - 3}x \, dx \\\\ ~~~~~~~~~~~~~\, = \frac14 \int_3^7 \left(4 - \frac3x\right) \, dx \\\\ ~~~~~~~~~~~~~\, = \left. \frac14 (4x - 3\ln|x|) \right\vert_3^7\\\\ ~~~~~~~~~~~~~\, = \boxed{4 + \frac34 \ln\left(\frac37\right)}[/tex]

Answer:

71.815<701.815

Step-by-step explanation:

Answer: 60 rides

Step-by-step explanation:

18/30% = (as fraction) 180/3

= 60

101011 in base 2 is equal to 43 in base 10

Answer:

x · 0.28 = 13.44

Equation: X multiplied by 0.28 = 13.44.

How to solve: Divide 13.44 ÷ 0.28 = 48.

Multiply to check. 48 x 0.28 = 13.44.

Give me a crown.

Midpoint formula : -

Midpoint calculation

The midpoint formula is a method used to locate the midway point between two coordinates on a graph. The midpoint of a line segment with endpoints A and B is the point that is precisely between A and B, that is, it is placed at the same distance from A and B, as shown in the illustration below.

The midpoint formula can be utilized when two points on a graph in the coordinate plane are known. The midpoint M of two points (x1, y1) and (x2, y2) is:

Notice that the midpoint formula includes calculating an average of the x- and y-values of two coordinates. The midway formula may be simpler to recall as a result. The sum of two number is equal to multiplying a number by 2. In a coordinate system, a line segment's midpoint is defined as the point midway between two points in the vertical and horizontal directions. This value is equivalent to the line segment's average x- and y-coordinates. It should be rather simple to recall the midway formula if you keep this in mind.

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Answer:

[tex]=4620000x[/tex]

Step-by-step explanation:

[tex]=1000000\cdot \:4.62x[/tex]
[tex]=4620000x[/tex]

Answer:

4620000

Step-by-step explanation:

4.62x10^6

1000000x4.62

Answer:

answer should be A. 2⅖

Step-by-step explanation:

you can find out by turning it into an improper fraction: =5×2+2/5

=10+2/5

=12/5

Answer:

See below

Step-by-step explanation:

Here is one possible mistake:

Let y= u = ( 2ax^2 +c)^2          expand

        4 a^2 x^4  + 4 a x^2 c   + c^2

  dy/ dx   then becomes  

16 a^2 x^3 + 8 a x c  <====== you have  8 a^2x^3 + 8axc  

   MAYBE ??

[tex]y = (2ax^2 + c)^2 (bx^2 - cx)^{-1}[/tex]

By the product rule,

[tex]\dfrac{dy}{dx} = \dfrac{d(2ax^2+c)^2}{dx} (bx^2-cx)^{-1} + (2ax^2+c)^2 \dfrac{d(bx^2-cx)^{-1}}{dx}[/tex]

For the first derivative on the right side, let [tex]u=2ax^2+c[/tex]. Then by the chain rule,

[tex]\dfrac{d(2ax^2+c)^2}{dx} = \dfrac{du^2}{dx} \\\\ ~~~~~~~~~~~~~~~~~~ = \dfrac{du^2}{du}\dfrac{du}{dx} \\\\ ~~~~~~~~~~~~~~~~~~ = 2u \dfrac{du}{dx} \\\\ ~~~~~~~~~~~~~~~~~~ = 2(2ax^2+c) \dfrac{d(2ax^2+c)}{dx}[/tex]

and by the power rule, this reduces to

[tex]\dfrac{d(2ax^2+c)^2}{dx} = 2 (2ax^2+c) (4ax) \\\\ ~~~~~~~~~~~~~~~~~~ = 8ax (2ax^2 + c)[/tex]

For the other derivative, let [tex]v = bx^2-cx[/tex]. Then

[tex]\dfrac{d(bx^2-cx)^{-1}}{dx} = \dfrac{dv^{-1}}{dx} \\\\ ~~~~~~~~~~~~~~~~~~~~ = \dfrac{dv^{-1}}{dv}\dfrac{dv}{dx} \\\\ ~~~~~~~~~~~~~~~~~~~~ = -v^{-2} \dfrac{dv}{dx} \\\\ ~~~~~~~~~~~~~~~~~~~~ = -(bx^2-cx)^{-2}\dfrac{d(bx^2-cx)}{dx}[/tex]

which reduces to

[tex]\dfrac{d(bx^2-cx)^{-1}}{dx} = -(bx^2 - cx)^{-2} (2bx - c)[/tex]

So one expression for the derivative we want is

[tex]\dfrac{dy}{dx} = 8ax (2ax^2 + c) (bx^2-cx)^{-1} - (2ax^2+c)^2 (bx^2 - cx)^{-2} (2bx - c)[/tex]

Answer is  f(x)= [tex]\frac{x^{2}+ 2x - 8 }{x - 5}[/tex]

vertical asymptote, the denominator must be contained (x−5)

and for zeros the numerator must be contained (x−2)

then we get,

So far f(x)= f(x)= [tex]\frac{ (x - 2)}{x - 5}[/tex]

​

For slant asymptote, quotient of numerator divided by denominator must be (x+4)

Therefore:

f(x)= [tex]\frac{(x + 4) (x - 2)}{x - 5}[/tex]

after solving this equation we get,

So f(x)= [tex]\frac{x^{2}+ 2x - 8 }{x - 5}[/tex]

​A vertical asymptote is a vertical line that guides the graph of the function but is not part of it. It can never be crossed by the graph because it occurs at the x-value that is not in the domain of the function. A function may have more than one vertical asymptote.

In Mathematics, a slant asymptote, also known as an oblique asymptote, occurs when the degree of the numerator polynomial is greater than the degree of the denominator polynomial. The slant asymptote gives the linear function which is neither parallel to x-axis nor parallel to the y-axis.

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The highest point is 14799 ft. higher than the lowest point.

From the information, the highest point in a country has an elevation of 14,291 feet. The lowest point in a country is at 508 fest below sea level.

The difference between the points will be:

= 14291 - (-508)

= 14291 + 508

= 14799 feet

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Answer:

formula for the derivative of x*lnx is equal to 1 + lnx.

Step-by-step explanation:

we need to find derivative of f(x) = x*lnx,

so we take the limiting value as x approaches x + h.

To simplify this, we set x = x + h,

and we want to take the limiting value as h approaches 0.

Now according to first derivative formula we have;

f'(x) = [tex]\lim_{h \to \zer0}[/tex]f(x+h) - f(x)]/[(x+h) - x]

[tex]\lim_{h \to \zer0}[/tex][ ln (1 + x) ] / x = 1

ln a - ln b = ln(a/b)

Using the above formulas, we have

d(xlnx)/dx = [tex]\lim_{h \to \zer0}[/tex][(x+h) ln(x+h) - xlnx]/[(x+h) - x]

= [tex]\lim_{h \to \zer0}[/tex][x ln(x+h) + h ln(x+h) - xlnx]/h

= [tex]\lim_{h \to \zer0}[/tex][x ln(x+h) - x lnx + h ln(x+h)]/h

= [tex]\lim_{h \to \zer0}\\[/tex][x(ln(x+h) - lnx) + h ln(x+h)]/h

=[tex]\lim_{h \to \zer0}[/tex][x ln [(x+h)/x] + h ln(x+h)]/h

=[tex]\lim_{h \to \zer0}[/tex][x ln (1+h/x) + h ln(x+h)]/h

=[tex]\lim_{h \to \zer0}[/tex] [x ln (1+h/x)]/h + limh→0 ln(x+h)

= [tex]\lim_{h \to \zer0}[/tex][ ln (1 + h/x) ] / (h/x) + limh→0 ln(x+h)

= 1 + lnx --- [Using limit formula [tex]\lim_{h \to \zer0}[/tex] [ ln (1 + x) ] / x = 1]

Hence, we have proved that the formula for the derivative of x*lnx is equal to 1 + lnx.

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Answer:

Step-by-step explanation:

In this section, we will determine the differentiate of xlnx using the first principle of derivatives, that is, the definition of limits. To derive the derivative of f(x) = xlnx, we take the limiting value as x approaches x + h. To simplify this, we set x = x + h, and we want to take the limiting value as h approaches 0. We will use the following formulas to prove the result:

f'(x) = limh→0[f(x+h) - f(x)]/[(x+h) - x]

limx→0 [ ln (1 + x) ] / x = 1

ln a - ln b = ln(a/b)

Using the above formulas, we have

d(xlnx)/dx = limh→0[(x+h) ln(x+h) - xlnx]/[(x+h) - x]

= limh→0[x ln(x+h) + h ln(x+h) - xlnx]/h

= limh→0[x ln(x+h) - x lnx + h ln(x+h)]/h

= limh→0[x(ln(x+h) - lnx) + h ln(x+h)]/h

= limh→0[x ln [(x+h)/x] + h ln(x+h)]/h

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The friend doesn't have a fever when the temperature increases by 1°C.

To convert Celcius to Fahrenheit,we have to multiply by 1.8 and add 32°.

This will be:

37°C = (37 × 1.8) + 32

= 98.6

When we add 1°, we will get 99.6.

Therefore, the friend doesn't have a fever when the temperature increases by 1°C.

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The area of the rectangular pink border is of 400 cm².

The area of a rectangle of dimensions l and w is given by the multiplication of the dimensions, as follows:

A = lw.

Hence, the total area is given by:

A = 30 x 20 = 600 cm².

The area of the white region is given by:

A = (30 - 2 x 5) x (20 - 2 x 5) = 20 x 100 = 200 cm².

Hence the area of the pink border is:

600 cm² - 200 cm² = 400 cm².

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Answer:

175

Step-by-step explanation:

because 7/8 of 200 is 175

Step-by-step explanation:

(1)

FP = FN

makes the triangle FNP an isoceles triangle (both legs have the same length). and that means both angles of these equal legs with the third side (PN) must be equal.

therefore, the angle N = P2 = 56°.

and we know that the angle P = P1 + P2 = 68 + 56 = 124°.

LE = LM

makes the triangle ELM an isoceles triangle. because of that, both angles of these 2 legs with the third side (ME) are equal.

therefore, M1 = E1 = 62°.

the fact that the sum of all angles in a triangle is always 180° gives us the angle L

180 = 62 + 62 + angle L = 124 + angle L

56° = angle L

because angles L and P are supplementary (that means together they have 180°, which is true as 124 + 56 = 180), it means that LM || PN. as this pair of supplementary angles means that their connecting line LP is intersecting the lines LM and PN at the same angles, which makes LM parallel to PN.

and as angle N = angle L (56°), this also proves that MN is parallel to LP (as now the line PN intersects LP and MN at the same angles and N and P are supplementary angles).

(2)

with the proof in (1) that we have 2 sets of parallel sidelines (LP || MN, LM || PN), this makes LMNP per basic definition a parallelogram.

Step-by-step explanation:

5.|12 - r| > 15

|12 - r| > 15/5

|12 - r| > 3

12 - r < -3 or 12 - r > 3

-r < -3 - 12 or -r > 3 - 12

-r < -15 or -r > -9

r > 15 or r < 9

Answer: 1L = 1000 mL

Step-by-step explanation:

1.     1 milligram (mg) is equal to 0.001 gram (gm), so 10mg = 0.01. The first choice is incorrect

2.    1 liter (L) = 1000 milliliter (mL) so the second choice is correct

3.    1 microgram (mcg) is equal to 0.001 milligram (mg), so the third                                                                 choice is incorrect.

4.    1 liter (L) = 1000 milliliter (mL), so the fourth choice is evidently                                        incorrect. (1000 L would be 1,000,000 mL)

Answer:

0

Step-by-step explanation:

[tex]n(S \cup T)=n(S)+n(T)-n(S \cap T) \\ \\ 15=15-n(S \cap T) \\ \\ n(S \cap T)=0[/tex]

The expression √4x  using rational exponents ( 4x )^{\frac{1}{2} } .

What is rational exponents?

What is Integer Exponents?

√4x  

use [tex]\sqrt[n]{a^{x} } = a^{x/n}[/tex]

to rewrite

√4x   = [tex]( 4x )^{\frac{1}{2} }[/tex]

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===========================================

Explanation:

Use the formula

a & b/c = (a*c + b)/c

So,

9 & 3/5 = (9*5+3)/5 = (45+3)/5 = 48/5