The museum of natural history has an auditorium that can seat 200 people. A class of 45 students is seated in the auditorium for a lecture. What decimal represents the portion of the seats in the auditorium that are empty ?

Answer:

27

Step-by-step explanation:

In this case, because we have a polynomial where all x-values exist, we can plug the value (x=2) straight into the function:

[tex]\lim_{x \to \ 2} (2x^3+x^2+7)[/tex]

[tex]= 2(2)^3+(2)^2+7[/tex]

[tex]= 2(8)+4+7[/tex]

[tex]= 27[/tex]

The limit of (2x^3+x^2+7) as x approaches 2 equals 27, which makes sense since the value of (2x^3+x^2+7) at x = 2 is 27.

Answer:

Looking Ahead to Calculus: Lessons 1-5 Quick Check Answers

Lesson 1

Q1 B. -21

Q2 D. 4

Q3 D. 4 (yes, again)

Q4 B. lim f(x) = 5 [x→3+] ;

D. lim f(x) = 6 [x→3-] ;

F. lim f(x) [x→3] does not exist...

Lesson 2

Q1 A. lim x = a [x→a] ;

B. lim a = a [x→a];

D. lim x = 5 [x→5]

Q2 D. 16

Q3 B. 10a

Q4 D. 3

Lesson 3

Q1 A. -1

Q2 D. 1

Q3 B. It is discontinuous because there is a value a for which f(a) is not defined.

Q4 D. It is discontinuous because there is a value a such that lim f(x) [x→a] does not exist.

Lesson 4

Q1 D. 3

Q2 A. -13

Q3 C. y = -2x + 6

Q4 C. f'(a) = 8a + 2

Lesson 5

Q1 C. 2

Q2 D. v(t) = 8t - 2

Q3 B. 902 mi./min.

Q4 A. The car is slowing down at a rate of 10 mi./h^2.

Have a great summer

Answer:

x = 3, x = 11

Step-by-step explanation:

Since PR is an angle bisector then it divides the opposite side into segments which are proportional to the other 2 sides, that is

[tex]\frac{PQ}{PS}[/tex] = [tex]\frac{QR}{SR}[/tex] , substitute values

[tex]\frac{x+1}{16}[/tex] = [tex]\frac{x-2}{x+1}[/tex] ( cross- multiply )

(x + 1)(x + 1) = 16(x - 2) ← expand left side using FOIL

x² + 2x + 1 = 16x - 32 ( subtract 16x - 32 from both sides )

x² - 14x + 33 = 0 ← in standard form

(x - 3)(x - 11) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 11 = 0 ⇒ x = 11

Answer: Only B

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

Explanation:

For situation A,

The pairing (x,y) tells us what a certain student likes in terms of color.

For example, the point (Allen, Red) tells us that Allen likes the color red. We could also have (Allen, Green) telling us he also likes green. Because the input "Allen" maps to more than one output, this means situation A is not a function. A function is only possible if any given input maps to exactly to one output. The input must be in the domain. The domain in this case is the set of all students in the classroom.

In contrast, Situation B is a function because a student will only have one favorite math teacher. I'm interpreting this to mean "number one favorite" and not a situation where a student can select multiple favorites.

Answer:

You can make pancakes 15 times.

Step-by-step explanation:

Assuming you meant 2/3 cup and not 23! In that case the answer would be 15. Divide 10 by 2/3 to get there!

Answer:

Step-by-step explanation:

1 yard is about 36 inches.

A square yard in square inches will therefore be:

= 36 * 36

= 1,296 inch²

He needs 497 square inches of gray fabric. In square yards that will be:

= 497/1,296

= 0.38 yard² of gray material

He needs 746 square inches of yellow:

= 746/1,296

= 0.58 yard² of yellow.

Answer:

dbbxnxnznndn

Step-by-step explanation:

hdhhdhdhdjxmdk

Answer:

$1032.60

Step-by-step explanation:

Given data

salary = $950 every two weeks

tax rate = 8%

let the initial pay be x

and let the pay after tax deduction be p

p= x-8/100x

Hence the equation for his pay is

[tex]p=x-0.08x-------------1[/tex]

subsitute

950=x-0.08x

950= 0.92x

divide both sides by 0.92

x= 950/0.92

x=$1032.60

The employee make $1032.60 every two weeks before taxes

Answer:

yes

Step-by-step explanation:

Answer:

blank1 = earth    blank2 = 483.08 billion feet

Step-by-step explanation:

Answer:

666666666666666666666666666666675915730995

.

Step-by-step explanation:

Answer:

Slope=-2  Y-Intercept= (0,5)

Step-by-step explanation:

Answer:

Slope is -1

Step-by-step explanation:

Slope is always the number before the x in these equations.

(wish I could help you with the graphing- some of the points are: (2,1) (1,2) (3,0) (4,-1) (-1,4) )

(hope this helps!)

Answer:

25 in

Step-by-step explanation:

Hypotenuse is the longest side in the right angle triangle. It is proven by the fact that the square of hypotenus is the sum of the squares of the two other sides.    

The hypotenuse of the Pythagorean triple 25 in, 15 in, 20 in is 25 in

The Pythagoras theorem is used to find the sides of a right angle triangle. The formula below is used to find the sides of a right angle triangle(Pythagoras's theorem) is represented below

where

c = hypotenuse

a and b are either opposite or adjacent sides

A right angle triangle is a triangle that has one of its angles as 90°.

A right angle triangle has the following sides :

The longest side of a right angle triangle is the hypotenuse. Base on the Pythagorean triple, the hypotenuse is 25 inches because its the longest side.

read more: https://brainly.com/question/25079188?referrer=searchResults

Answer: x=7

Step-by-step explanation:

(5x-40)+7 = 2

5x-33 = 2

5x = 35

x = 35/5

x = 7

Answer:

x = 7

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

5(x - 8) + 7 = 2

Step 2: Solve for x

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Here we see that 2 does indeed equal 2.

∴ x = 7 is the solution to the equation.

Answer:

18.85 inches

Step-by-step explanation:

Eq: 2πr

D/2=R

6/2=3 inches

2π3

=18.85 inches

OR

πd

6π

=18.85 inches

Answer:

m= -2/5

Step-by-step explanation:

formula:

m = (y2 - y1) / (x2 - x1)

Answer:

3/8

Step-by-step explanation:

the answer is 3/8 because u are muliplying 1/2 and 3/4 and 1×3 is 3 and 2×4 is 8 3/8

Answer:

y =(-3/2)x

Step-by-step explanation:

(0,0) ; (2 , -3)

Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

         [tex]= \frac{-3-0}{2-0}\\\\= \frac{-3}{2}[/tex]

Equation: y - y1 =m(x-x1)

y - 0 = [tex]\frac{-3}{2}(x- 0)\\[/tex]

[tex]y = \frac{-3}{2}x[/tex]

Answer:

720 feet

A yard is equivalent to 3 feet, so 1 yard = 3 feet.

240 yards * 3 = 720 feet

Step-by-step explanation:

Answer:

240 yards=720feet

Step-by-step explanation:

Answer:

d, commutative property

Step-by-step explanation:

the commutative property states that the position and location of numbers in an equation can be swapped or moved, and the answer will remain the same. this only works for addition and multiplication, not subtraction and division.

Answer:

Difference = 36

Step-by-step explanation:

Given that,

The boiling point of Oxygen = -183

The melting point of Oxygen = -219

We need to find the temperature difference of the melting point and the boiling point.

Difference = boiling point - melting point

= -183-(-219)

= -183+219

= 36

Hence, the required temperature difference is 36.

Answer:

A

Step-by-step explanation:

A negative times a negative will always be a postive

Answer:

x = 11

y = 3

Step-by-step explanation:

In a parallelogram opposite sides are equal.

8x = 88

x = 88/8

x = 11

4y - 7 = y + 2

4y      = y + 2 + 7

    4y = y + 9

4y - y = 9

       3y =  9

         y = 9/3

        y = 3

Answer:

the equation says that energy and mass (matter) are interchangeable; they are different forms of the same thing.

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

so first we need to figure out how many money did she save

50*20% = 10 dollars

so she saved 10 dollars

then 50-10=40

so she paid 40 dollars