Define the following terms:

Answer:

The input of the function

Step-by-step explanation:

Answer:

a. 15 students

b. 32 students

c. 35 students

d. 34 students

e. 55 students

f. 67 students

Step-by-step explanation:

See attachment for complete question

Solving (a): Tricycle, Motorcycle and Car

This is the intersection of Tricycle, Motorcycle and Car.

From the attached Venn diagram, there are 15 students in this category

Solving (b): Tricycle and Motorcycle.

This is the intersection of Tricycle and Motorcycle.

From the attached Venn diagram, we observe the following data:

[tex]Tricycle\ and\ Motorcycle\ only =17[/tex]

[tex]All = 15[/tex]

[tex]Tricycle\ and\ Motorcycle = All + Tricycle\ and\ Motorcycle\ only[/tex]

[tex]Tricycle\ and\ Motorcycle = 15 + 17[/tex]

[tex]Tricycle\ and\ Motorcycle = 32[/tex]

Solving (c): Car and Motorcycle.

This is the intersection of Car and Motorcycle.

From the attached Venn diagram, we observe the following data:

[tex]Car\ and\ Motorcycle\ only = 20[/tex]

[tex]All = 15[/tex]

So:

[tex]Car\ and\ Motorcycle = All + Car\ and\ Motorcycle\ only[/tex]

[tex]Car\ and\ Motorcycle = 15 + 20[/tex]

[tex]Car\ and\ Motorcycle = 35[/tex]

Solving (d): Car and Tricycle.

This is the intersection of Car and Tricycle.

From the attached Venn diagram, we observe the following data:

[tex]Car\ and\ Tricycle\ only = 19[/tex]

[tex]All = 15[/tex]

So:

[tex]Car\ and\ Tricycle = All + Car\ and\ Tricycle\ only[/tex]

[tex]Car\ and\ Tricycle = 15 + 19[/tex]

[tex]Car\ and\ Tricycle = 34[/tex]

Solving (e): Car only

From the attached Venn diagram, we observe the following data:

[tex]Car\ only = 55[/tex]

Solving (e): Motorcycle only

From the attached Venn diagram, we observe the following data:

[tex]Motorcycle\ only = 67[/tex]

Answer:

The birth weight associated with the lowest 1% is 4.6 pounds.

Step-by-step explanation:

Let X represent the birth weights of babies.

It is provided that [tex]X\sim N(7.6,1.3^{2})[/tex]

It is also provided that many pre-mature births weights are in the lowest 1% of births.

Let x represent the births weights that are in the lowest 1% of births.

That is, P (X < x) = 0.01.

⇒ P (Z < z) = 0.01

The corresponding z-score is, z = -2.33.

Compute the value of x as follows:

[tex]z=\frac{s-\mu}{\sigma}\\\\-2.33=\frac{x-7.6}{1.3}\\\\x=7.6-(1.3\times 2.33)\\\\x=4.571\\\\x\approx 4.6[/tex]

Thus, the birth weight associated with the lowest 1% is 4.6 pounds.

Answer:

equivalent

Step-by-step explanation:

Equivalent means equal so equivalent expressions equal the same value.

Answer:check photo

Step-by-step explanation:

Divide 488 by 61 to find the unit rate.

488/61 = 8

You get 8 points for defeating each enemy.

Hope this helps

Answer:

An increase of $0.94

Step-by-step explanation:

Answer:

The answer is 10

Answer:

The snake would equal 160cm.

Step-by-step explanation:

Correct me if im wrong plz

Answer:

0.034

Step-by-step explanation:

10^-2 is 1 over 100 times 3.4

Answer:

4x4=shaggy

Step-by-step explanation:

Answer:

-9/14

Step-by-step explanation:

Have a good day <3

Answer:

-9/14

Step-by-step explanation:

-3/8 ÷ 7/12

Flip the second fraction and multiply

-3/8 x 12/7

You can cross-simplify

-36/56

-9/14

Hope this helped!

Answer:

392984

Step-by-step explanation:

Answer:

=130

Step-by-step explanation:

(2x) (5x+5) = 180

7x + 5 = 180

7x = 175

x = 25

5(25) + 5 = 125 + 5 = 130

Hope this helps (:

Answer:

$50

Step-by-step explanation:

Answer:

12

by-step explanation:

Answer:

10(3x + 4y)

Step-by-step explanation:

Answer:

Shop and save

Step-by-step explanation:

Answer:

You can buy 5 of the same apples at Shop and Save for $2.10.

Step-by-step explanation:

Answer:

5(2c+5)

I hope this helps

Answer:

x= -5

Step-by-step explanation:

5x + 10 = -15

subtract 10 from both sides

5x = -25

divide both sided by 5

x = -5

Hope this helps :)

Answer:

3

Step-by-step explanation:

he has 7/8 paper divided by 1/5 paper it takes to make the paper plane, it equals 3.5. Three whole ones

Answer:

this is your question

Step-by-step explanation:

please mark as brainliest

The slope of the linear function would be 1/6, [y] - intercept will be equal to -5 and [x] - intercept will be equal to 1/30.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written to express proportional relationship as -

y = kx  {k is constant}

We have a linear function f(x) that models a relationship in which the dependent variable decreases 3 units for every 2 units the independent variable increases. The value of the function at 0 is -5

Since the dependent variable decreases 3 units for every 2 units the independent variable increases, we can write -

3y = 1/2x

y = 1/6x

At [x] = 0, y = - 5

So -

y = (1/6)x - 5

Now -

slope = 1/6

[y] - intercept = - 5

y = 0 = (1/6)x - 5

(1/6)x - 5 = 0

1/6x = 5

x = 1/30

[x] - intercept = 1/30

Therefore, the slope of the linear function would be 1/6, [y] - intercept will be equal to - 5 and [x] - intercept will be equal to 1/30.

To solve more questions on Money and taxes, visit the link below-

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Answer:

0.667 and 66.67% rounded

Step-by-step explanation:

2/3 = 0.66666 repeating which can be rounded to 0.667

2/3 = 66.6666% repeatinf which can be rounded to 66.67%

                                    _

Answer: Decimal = 0.6  Percent = 66.67%

Step-by-step explanation: The line above the 6 in 0.6 stands that it repeats over and over again, and the percent is 66.67% because if you divide 100/3x2, you get 66.67.

Answer:

Divide 9944 by 12 feet per second

828.666 or 828.7

Step-by-step explanation:

9514 1404 393

Answer:

  829 ft/s

Step-by-step explanation:

Multiply by a conversion factor that cancels the units you don't want and gives you the units you do want.

  [tex]\dfrac{9944\text{ in}}{\text{s}}\times\dfrac{1\text{ ft}}{12\text{ in}}=\dfrac{828.\overline{6}\text{ ft}}{\text{s}}\approx\boxed{829\text{ ft/s}}[/tex]

Answer:

355.923 cubic feet per month

Step-by-step explanation:

Units Conversions

We need to convert from pints/day to cubic feet/month. Two basic conversions are needed:

1 US pint = 0.0167101 cubic foot

1 month = 30 days (average)

710 pints are equivalent to 710 * 0.0167101 = 11.8641 cubic feet

That volume corresponds to a daily flow. For a monthly flow, multiply by 30:

355.923 cubic feet per month

Answer:

42.5

Step-by-step explanation:

Point for correct score  = [tex]\frac{11}{2}[/tex]  = 5.5

Point for incorrect score = [tex]\frac{1}{2}[/tex] = 0.5

Unknown:

Final score = ?

Solution:

Number of correct score  = 8

   Points gained  = 8 x 5.5 = 44

Number of incorrect score  = 3

  Points lost  = 3 x 0.5  = 1.5

His final score  = 44 - 1.5  = 42.5

Answer:

a) x = 798   is the quantity that maximizes the profit

b)po(x) = 401 $/unit

c)P(max ) = 636105 $

Step-by-step explanation:

The weekly demand function is equal to the price by unit and the Revenue function is weekly demand times quantity of units then:

R(x) = p(x) * x

R(x) = ( 800 - 0,5*x ) * x

R(x) = 800*x - 0,5*x²

The equation for the profit is:

P(x) = R(x) - C(x)

P(x) = 800*x - 0,5*x² - ( 300 + 2*x)

P(x) = 798*x - 0,5*x² - 300

a) P(x) = 798*x - 0,5*x² - 300

Taking derivatives on both sides of the equation:

P´(x) = 798 - x

If P´(x) = 0     then    798 - x = 0

x = 798   is the quantity that maximizes the profit

b) Selling price for the optimal quantity is:

p(x) = 800 - 0,5*x

p(x) = 800 - 0,5* 798

po (x) = 800 - 399

po(x) = 401 $/unit

c) Pmax = ?

P(x) = 798*x - 0,5*x² - 300    by subtitution of  x = 798

P(max) = 636804 - 399 - 300

P(max ) = 636105 $

a) The quantity that will maximize profit is [tex]100 \ units[/tex].

b) The selling of at this optimal quantity is [tex]\[/tex][tex]750[/tex] per unit.

c) So, the maximum profit is [tex]\[/tex][tex]25000[/tex].

A demand function is a mathematical equation that expresses the demand for a product or service as a function of its price and other factors such as the prices of the substitutes and complementary goods, income, etc.

The given demand function,

[tex]P=800-\frac{1}{2}x[/tex]

So, the revenue function is,

[tex]R(x)=p.x\\R(x)=800-x-\frac{1}{2}x^{2}[/tex]

[tex]\Rightarrow[/tex]Average cost is

[tex]\bar{C}=300+2x[/tex]

So, the total cost function is,

[tex]C\left ( x \right )=\bar{C}.x \\ C\left ( x \right )=300x+2x^{2}[/tex]

a) Profit function:

[tex]P\left ( x \right )=R\left ( x \right )-C\left ( x \right ) \\ =800x-\frac{1}{2}x^{2}-300x-2x^{2} \\ P\left ( x \right )=500x-\frac{5}{2}x^{2}[/tex]

For maximum,

[tex]{P}'\left ( x \right )=0 \\ 500\left ( 1 \right )-\frac{5}{2}\left ( 2x \right )=0 \\ 500-5x=0 \\ x=100[/tex]

b) Selling Price:

[tex]P=800-\frac{1}{2}x \\ at \ x=100 \\ P=800-\frac{1}{2}\left ( 100 \right ) \\ =\$ 750[/tex]

c) Maximum Profit:

[tex]P\left ( x \right )=500x-\frac{5}{2}x^{2} \\ P\left ( 100 \right )=500\left ( 100 \right )-\frac{5}{2}\left ( 100 \right )^{2} \\ P\left ( 100 \right )=\$ 25000[/tex]

Learn more about of Demand Function: https://brainly.com/question/25938253

Answer:

-13

Step-by-step explanation:

see if good