18) The profit that the vendor makes per day by selling x pretzels is given by the function
P(x) = -0.004x2 + 2.8x - 100. Find the number of pretzels that must be sold to maximize profit.
A) 390 pretzels
B) 350 pretzels
C) 700 pretzels
D) 1.4 pretzels

The rate of change of the volume of the sphere is 100,530.96 mm^3/s

How to calculate rate of change of the volume of the sphere?

Given,

radius = r = 80 / 2 = 40 mm

rate of change radius = [tex]\frac{dr}{dt}[/tex] = 5 mm/s

Formula to calculate volume of the sphere is

[tex]V = \frac{4}{3}\pi r^{3}[/tex]

Differentiating the volume formula and we get new formula to calculate rate of change of the volume.

[tex]\frac{dV}{dt} = \frac{4}{3}\pi 3r^{2}\frac{dr}{dt}[/tex]

Simplify to

[tex]\frac{dV}{dt} = 4\pi r^{2}\frac{dr}{dt}[/tex]

Now, we put the given value to formula and calculate it

[tex]\frac{dV}{dt} = 4\pi (40)^{2}(5)[/tex]

[tex]\frac{dV}{dt} = 100,530.96[/tex] mm^3/s

Thus, the rate of change of the volume of the sphere is 100,530.96 mm^3/s

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Step-by-step explanation:

look at where the dotted line is : it is vertical at x = -3.

that is automatically is equation : x = -3.

now, look at where the shaded side of that line is - to the left or to the right of the line ?

it is to the left of the line. and that message all values smaller than x = -3. but not equal indicated by the dotted line (that means the line itself is not included).

so, this is described by x < -3.

therefore, the first answer option is out.

now, look at the solid line.

what is the y-intercept (the y- value when x = 0) ?

when x = 0, the y-value is -1.

and everything to the left and below of the line is included (incl. the line itself, hence the solid line), so, the line inequality is then (just given by the available choices)

y <= -x - 1

and the 3rd answer option is therefore correct.

Answer:

[tex]\begin{cases}x < -3\\y \leq -x-1\end{cases}[/tex]

Step-by-step explanation:

When graphing inequalities:

From inspection of the given graph, there is a dashed line at x = -3 with shading under the line (to the left).

Therefore, the inequality that represents this is:  

The solid line has a negative slope.  For each decrease of 1 unit in the y-direction, the x-values increase by 1 unit.  Therefore, the slope of this line is -1.  

From inspection of the given graph, the y-intercept of the solid line is -1.

Therefore, the equation of this line is  y = -x - 1.  

As the shading is under the line, the inequality that represents this is:

Therefore, the system of linear inequalities that represents the graph is:

[tex]\begin{cases}x < -3\\y \leq -x-1\end{cases}[/tex]

Answer: The answer to that would be 3.

Step-by-step explanation: So 5 / 1  2/3 = 3

Sorry my handwriting is so sloppy! Hope it helps!

Answer:

Of the homeowners, half have either a dog or a cat.

Step-by-step explanation:

Since 2/3 of all homeowners have a pet, and 3/4 of those have dogs or cats, we simply need to multiply 2/3 and 3/4 to see what fraction of all homeowners have a dog or a cat.

2/3 x 3/4 = 6/12

6/12 = 1/2

We can double check this. If there are 60 homeowners, and 2/3 have a pet, that would mean that 40 of those homeowners have a pet.

If 3/4 of the 40 homeowners have either a dog or a cat, that would equate to 30 homeowners having either a dog or a cat.

Since 30 is half of 60, this would mean that 1/2 of the 60 homeowners have a dog or cat!

Hope this answer helped you!

Answer:

D

Step-by-step explanation:

First, we should find the equations of the two lines. The red line is just horizontal, and represents y = 4 while the blue line intersects the y-axis at -4 and every time it goes right one, it goes up 4, so it has a slope of four(also it looks kinda steep, so it cannot have a slope of 1/4). This means the equation is y = 4x - 4.

Notice the red line is dashed, that means the inequality is either less than or greater than. Also, the shaded part is below the vertical line, enclosing all the values of y less than 4, so the first inequality would be y < 4.

The blue line is solid, so it is either greater than or equal to or less than or equal to. To find out which one, we check to se where the point (0, 0) fits in:

y ? 4x - 4

0 ? 0 - 4

0 ? -4

Only a greater than or equal to sign would fit in: 0 ≥ -4

This means the answer is:

y < 4

y ≥ 4x - 4

which is option D

Answer:

Step-by-step explanation:

1)

The equation of a straight line:

y = k·x + b

x = 0

b = y = - 4

k = (y - y₀) / (x - x₀) = ( 4 - (-4)) / (2 - 0) =  8 / 2 = 4

y = 4·x - 4

2)

The equation of a straight line:

y = 4

3)

Shaded area:

y ≤ 4

y ≥ 4x - 4

Right answer:

D.

y ≤ 4

y ≥ 4x - 4

Answer:

40;100

step by step explanation:

Answer:

Step-by-step explanation:

so use the properties of powers, recall that powers like [tex]x^{2^{2} }[/tex] is the same as [tex]x^{2} *x^{2}[/tex] which can also be written as  [tex]x^{2*2}[/tex] = [tex]x^{4}[/tex].

I want to make this clearer.

[tex]x^{3^{3} }[/tex] = [tex]x^{3}[/tex]  * [tex]x^{3}[/tex] * [tex]x^{3}[/tex]  = [tex]x^{3*3*3}[/tex] =[tex]x^{27}[/tex]

I'm not sure if that's making it clearer or not.

so for your question  of  [tex](8x^{6}) ^{2/3}[/tex]  we can rewrite it to look like the above multiplication of powers

[tex]8x^{6*(2/3)}[/tex]

[tex]\frac{6}{1}[/tex] * [tex]\frac{2}{3}[/tex] = [tex]\frac{12}{3}[/tex]  = 4

[tex]8x^{4}[/tex]

The first step in simplifying is to apply that outer exponent of [tex]\frac{2}{3}[/tex] to each factor inside the parentheses.

      [tex]\left(8\cdot x^6\right)^{2/3} = \left(8\right)^{2/3} \cdot \left(x^6\right)^{2/3}[/tex]

Now using the concept that [tex](a)^{m/n} = \sqrt[m]{a^n}[/tex] for positive real numbers a and integers m and n, we can evaluate the first part:

       [tex](8)^{2/3} = \sqrt[3]{8^2} = \sqrt[3]{64} =4[/tex]

For the second part, we use the power-to-a-power rule, that says [tex](a^m)^n = a^{m\cdot n}[/tex]:

    [tex]\left(x^6\right)^{2/3} = x^{6\cdot \frac{2}{3}} = x^4[/tex]

Putting that all together, we have

    [tex]\left(8 x^6\right)^{2/3} = \left(8\right)^{2/3} \cdot \left(x^6\right)^{2/3} = 4x^4[/tex]

Answer:

4

Step-by-step explanation:

The answer really just popped into my head.

4^2 + 4^2 = 32

4x4=16

The average rate of change between year 1 and year 10 is given as follows:

4.3 thousand cars a year.

The average rate of change of a function is obtained by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

In this problem, the function is presented as follows:

C(x) = 0.15x³ - 3.28x² + 23.75x - 2.1.

The interval is:

[1,10], hence a = 1, b = 10.

At x = 1, the numeric value is found replacing each instance of x by 1, hence:

C(1) = 0.15(1)³ - 3.28(1)² + 23.75(1) - 2.1 = 18.52 thousand cars.

At x = 10, the numeric value is found replacing each instance of x by 10, hence:

C(10) = 0.15(10)³ - 3.28(10)² + 23.75(10) - 2.1 = 57.4 thousand cars.

Then the average rate of change is obtained as follows:

r = (57.4 - 18.52)/(10 - 1) = 4.3 thousand cars a year.

The problem is given by the image shown at the end of the answer.

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The solution to the inequality expression is f >-3

From the question, we have the following parameter that can be used in our computation:

-2f - 3.7 < 2.3

Add 3.7 to both sides of the expression

This gives

-2f < 6

Divide both sides of the expression by -2

So, we have the following representation

f >-3

Hence, the solution is f >-3

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The interest on the loan is $1200.

Given,

In the question:

You get a loan from the loan star bank to help pay for your home.

and, if you borrowed $12,000 at 10% for one year.

To find the interest on the loan.

Now, According to the question;

Based on the given conditions:
Formulate:

Borrowed= $12,000

At 10% for one year

12000 x 10%

Convert percentage into decimal

12000 x 0.1

calculate the product or quotient:

= 1200

Hence, The interest on the loan is $1200.

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The required equation model is y =  -(4.4/1009)x + 16, its slope is -(4.4/1009), and the y-intercept of the line of fit is 16.

The given table shows the amounts of storage left y 7 (in gigabytes) on a music-playing device when there are x songs on MTR the device.

As per the given table, take two points (0, 16) and (1009, 11.6)

The required equation will be as:

y - 16 = [(11.6 - 16)/(1009-0)](x-0)

y - 16 = -(4.4/1009)x

y =  -(4.4/1009)x + 16

The above equation models the amount of storage left as a function of the number of songs.

Here slope is -(4.4/1009), and y-intercept is 16

Therefore, the required equation model is y =  -(4.4/1009)x + 16, its slope is -(4.4/1009), and the y-intercept of the line of fit is 16.

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Joseph removes 5/8 gallon of white paint from a can.The amount of paint in the can  = - 2.8 gallons

Step-by-step explanation:

Let X be the starting amount of paint in the can, in gallons.

"Removes 5/8 gallon" can be written -(5/8)gal

"Adds 3/8 gallon" becomes +(3/8)gal

The result is :  X - (5/8)gal + (3/8)gal = Remaining Paint (gallons)

Consolidating:  Remaining (gallons) = X - (2/8)gal

If we want the overall increase/decrease, subtract the initial volume:

Initial - Remaining = Change in amount of paint in can

Change =  (X-(2/8)gal) - X = - (2/8) gallons

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Answer:

Step-by-step explanation:

Emma's age= x

Kate's age= x-12

sum of their ages=24

so Emma's age= 24-12

x=24-12

x=12

Emma's age=12

By using some exponent properties we will get:

2*(1/b)^15

Remember that the product of exponents can be written as:

(a^x)*(a^y) = a^(x*y)

In this case, we have the expression:

2*b^(-1.5)*b^10

Using the above property we can rewrite:

2*b^(-1.5)*b^10 = 2*b^(-1.5*10) = 2*b^(-15)

And a negative exponent means that we need to take the inverse of the base, then:

2*b^(-15) = 2*(1/b)^15

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Answer:

alternate interior angles theorem

Step-by-step explanation:

alternate interior angles theorem states that, if 2 parallel lines and a transversal form alternate interior angles, then, said angles are congruent.

The values of m<1, m<2, m<3, m<4, m<5, m<7, m<8 are given by 49, 131, 49, 131, 49, 49, 131 respectively.

Given the measure of angle 6 is 131.

We can see that from the figure, angle 6 and angle 2 are corresponding angles and angle 6 and angle 4 are alternative angles.

So, angle 2 = angle 6 = 131

angle 4 = angle 6 = 131

Since angle 1 and angle 4; angle 2 and angle 3 are Linear pairs. So.

angle 3 = 180 - angle 2  = 180-131 = 49

angle 1 = 180 - angle 4 = 180-131 = 49

Since, angle 1 and angle 5; angle 4 and angle 8; angle 3 and angle 7 are corresponding angles to each other.

angle 5 = angle 1 = 49

angle 7 = angle 3 = 49

angle 8 = angle 4 = 131

Hence the values of m<1, m<2, m<3, m<4, m<5, m<7, m<8 are given by 49, 131, 49, 131, 49, 49, 131 respectively.

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Value of angle T is 60°, angle U is 60°, TS is 13 cm and SU is 22.49 cm.

Given in question,

Triangle STU,

TU = 13 cm

∠S = 60°

ST = TU

    = 13 cm

∠U = ∠S    (Their sides are equal)

     = 60°

∠S + ∠T + ∠U = 180°

60 + ∠T + 60 = 180

      ∠T + 120 = 180

                ∠T = 180 - 120

                      = 60

Hence, ∠T is 60°.

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Answer:

f ≤ - [tex]\frac{19}{3}[/tex]

Step-by-step explanation:

8 - (- 4f - 3 ) ≤ - f - 8 + 2f ← distribute parenthesis on left side by - 1

8 + 4f + 3 ≤ f - 8

4f + 11 ≤ f - 8 ( subtract f from both sides )

3f + 11 = - 8 ( subtract 11 from both sides )

3f ≤ - 19 ( divide both sides by 3 )

f ≤ - [tex]\frac{19}{3}[/tex]

Step-by-step explanation:

if there is nothing missing, we have

x + 25/-8 = -6

in order to compare or add or subtract fractions, we need to bring them all to the same denominator (bottom part).

remember, integer numbers are fractions too. like here

-6 = -6/1

25/-8 = -25/8

so, how can we bring -6/1 to .../8 ?

by multiplying 1 by 8.

but we cannot multiply only the denominator by 8. otherwise we would suddenly have

-6/8

and is -6/8 = -6/1 ? no, certainly not.

to keep the original value of the fraction we have to do the same multiplication also with the numerator (top part).

so, we actually do

-6/1 × 8/8 = -48/8

with this little trick we have now .../8 to operate with, and our transformed fraction has still the same value

-6/1 = -48/8 indeed.

so, we have

x + -25/8 = -48/8

x - 25/8 = -48/8

x = -48/8 + 25/8 = -23/8

Answer:127 degrees

Step-by-step explanation: 180-74 = 106 106+21 = 127 180-127 = 53 180-53 =127

If h(x)=(fog)(x) then h'(3) = 12.

Given:

Let f and g be differentiable functions such that f(3)=5,g(3)=7,f'(3) = 13, g'(3) = 6,f'(7) = 2 and g'(7) = 0

h(x)=(fog)(x)

h(x) = f(g(x))

h'(x) = f'(g(x)) * g'(x)

h'(3) = f'(g(3) * g'(3)

= f'(7) * 6

= 2*6

= 12

Therefore If h(x)=(fog)(x) then h'(3) = 12.

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Answer:

[tex]y=-7x+6[/tex]

Step-by-step explanation:

1 ) Our given equation is [tex]Y\left(x\right)+8=-7\left(x-2\right)[/tex]

2 ) We can now graph this equation ( desmos is a good online graphing calculator ). The graph is shown in the attachment...

3 ) Now that the equation has been graphed we can see that the slope intercept form is [tex]y=-7x+6[/tex]

Hope this helps! :)

Answer:

The length is 12

The area is 72[tex]cm^{2}[/tex]

Step-by-step explanation:

3x + 7 = 5x -17  Subtract 3x from both sides

7 = 2x -17  Add 17 to both sdies

24 = 2x  Divide both sides by 2

12 = x

Area = length times witdth

Area = 6(12) = 72

Answer:

Step-by-step explanation:

part a):

6(3x+7)=6(5x-17)

part b):

18x+42=30x-102

42+102=30x-12x

144=12x

x=144/12

x=12

area = l x b

area = 6x{5(12)-17}

=6x(60-17)

=6x43

area=258cm2

Please mark as brainliestt :)))

Step-by-step explanation:

a) 100

b)45

trust me it will helps you

Answer:

x = 40

Step-by-step explanation:

for m and n to be parallel then

2x and 80 are alternate angles and congruent , so

2x = 80 ( divide both sides by 2 )

x = 40

Answer:

Step-by-step explanation:

Answer:

x = - 2 ± [tex]\sqrt{\frac{19}{3} }[/tex]

Step-by-step explanation:

3x² + 12x = 7 ← factor out 3 from each term on the left side

3(x² + 4x) = 7

to complete the square

add/ subtract ( half the coefficient of the x- term)² to x² + 4x

3(x² + 2(2)x + 4 - 4) = 7

3(x + 2)² - 12 = 7 ( add 12 to both sides )

3(x + 2)² = 19 ( divide both sides by 3 )

(x + 2)² = [tex]\frac{19}{3}[/tex] ( take square root of both sides )

x + 2 = ± [tex]\sqrt{\frac{19}{3} }[/tex] ( subtract 2 from  both sides )

x = - 2 ± [tex]\sqrt{\frac{19}{3} }[/tex]