A study of the effects of acid rain on trees in the Hopkins Forest shows that 25 of 100 trees sampled exhibited some sort of damage from acid rain. This rate seemed to be higher than the 15% quoted in a recentEnvironmetricsarticle on the average proportion of damaged trees in the Northeast. Does the sample suggest that trees in the Hopkins Forest are more susceptible than trees from the rest of the region

Answer:

Step-by-step explanation:

After graphing the function f(x) = [tex]4(\frac{1}{2})^{x}[/tex]  we can see that the correct graph is the middle one in the picture. This is because with an x-input of 1 the value of 1/2 will stay the same and when multiplied by 4 it would give us a y-coordinate of 2 as seen in the middle graph. The y-coordinate keeps decreasing exponentially by half for every increase in the x-coordinate. A zoomed-in version of the graph can be seen in the attached picture below for a better understanding.

Answer:

B' (- 7, 6 )

Step-by-step explanation:

Given the translation rule

(x, y ) → (x + 2, y + 5 )

This means add 2 to the original x- coordinate and add 5 to the original y- coordinate, then

B (- 9, 1 ) → B' (- 9 + 2, 1 + 5 ) → B' (- 7, 6 )

Answer:

Step-by-step explanation:

perimeter of rectangle=2(length + breadth)

=2(2p+q+p)

=2(3p+q)

=2*3p+2*q

=6p+2q cm

Step-by-step explanation:

Hey there!

From the figure;

Length (l) = 2p + q cm

Base (b) = pcm

Now;

Perimeter (p) = 2(l+b)

P = [2(2p+q) + p]

or, P = 2(3p+q)

or, P = 6p + 2qcm.

Therefore, perimeter (p) = 6p+2q cm.

Hope it helps!

Answer:

n = (1/2)(-1 ± i√2)

Step-by-step explanation:

Among the several ways in which quadratic equations can be solved is the quadratic formula.  Putting to use the coefficients {12, 12, 9}, we obtain the discriminant, b^2 - 4ac:  12^2 - 4(12)(9) = 144 - 432 = -288.  The negative sign of this discriminant tells us that the quadratic has two unequal, complex roots.  These roots are:

      -b ± √(discriminant)

n = ---------------------------------

                 2a

Here we have:

      -12 ± √(-288)           -12 ± i√2√144          -12 ± i12√2

n = ----------------------  =  ------------------------ =  --------------------

            2(12)                             24                           24

or:

n = (1/2)(-1 ± i√2)

Answer:

 [tex]option \ C[/tex]  [tex]3\frac{1}{3}[/tex]

Step-by-step explanation:

[tex]\frac{|2a| - b}{3} \ , \ given \ a = \ 7 \ , \ b \ =\ 4\\\\\frac{|2 \times 7| - 4}{3} = \frac{14 - 4}{3} = \frac{10}{3} = 3\frac{1}{3}[/tex]

Answer:

8!!

Step-by-step explanation:

5+3

Answer:

-11 is the answer

Answer:

f(x) and g(x) are closed under multiplication because when multiplied, the result remains a polynomial.

Step-by-step explanation:

First, to be closed means that once an operation has commenced, the result is a polynomial, just like the two original ones.

When polynomials are multiplied, exponents simply add together, and constants are multiplied. A polynomial is a finite sum of terms in which all variables have whole numbered exponents.

In this scenario, when we multiply polynomials, exponents are solely added together, and one whole number plus another is still a whole number. Similarly, constants multiplied by constants stay as constants, and constants multiplied by variables keeps it in polynomial form. (e.g. 3 * x² makes it 3x², and 3x² is fine in a polynomial).

Therefore, given these facts, f(x) and g(x) are closed under multiplication because when multiplied, the result remains a polynomial.

Answer:

D: (4, 6)

Step-by-step explanation:

undefined slope is when the line is vertical

so we are given a point (4, -1)

the best point that will make the slope undefined is D because it will make a vertical slope

1, 2, 3, 4, 5, 6, 7, 8, i don't know, and i haven't ate, 9, 10, 11, 12, this really sucks cuz ur on ur own :(

Answer:

C

Step-by-step explanation:

The length of each side of the square is (3x-2) units

The dimensions of the rectangle are (5x + 4y) and (5x -4y) units

From the question, we are to factor out the given expression for the area of the square

The expression is

9x² − 12x + 4

Factoring

9x² − 12x + 4

9x² −6x -6x + 4

3x(3x -2) -2(3x-2)

(3x -2)(3x -2)

Hence, the length of each side of the square is (3x-2) units

Part B:

The given expression is

25x² − 16y²

Factoring

25x² − 16y²

By difference of two squares, we get

(5x + 4y)(5x -4y)

Hence, the dimensions of the rectangle are (5x + 4y) and (5x -4y) units

Learn more on Factoring an expression here: https://brainly.com/question/11660720

#SPJ1

Answer:â

Step-by-step explanation:

f(x)+g(x)=3x^2-14-12x+4=3x^2-12x-10

Answer:

12

Step-by-step explanation:

The expression 3c + 24 represents the amount of cookies you sell and the expression 5c represents the amount of cookies your sister sells. If we want to find when they become equal, we must set them equal to each other:

3c + 24 = 5c

24 = 2c

12 = c

Therefore, the answer is 12.

Answer:

Step-by-step explanation:

Answer:

72π (I think)

Step-by-step explanation:

Think of it in terms of the entire circle. A semi-circle is just half a circle, so the area of a semicircle will be half of the area of the entire circle. The radius of the semicircle is 6, so the radius of the whole circle is 12. Then, we can do [tex]\frac{pi*r^{2} }{2}[/tex] to get the area of the semicircle is 72π. I'm pretty sure that's right. Let me know if I made a mistake somewhere.

Answer: A,B

Step-by-step explanation: the numbers constantly add up only by 218 or 1240 , C and D would not be correct because the rate of change increases as will with the total sum after each period of time

also tiny hint, if you were to draw an X,Y axis graph, A and B would be a straight line while C and D are curved up-wards

Answer:

A

Step-by-step explanation:

A zero in a polynomial function is what the variable is equal to to make the function equal to 0. In the graph, there is only one point that is on the x, 0. Meaning there is only one zero.

Answer:

Answer:

540 g flour

4 tsp baking powder

8 tbsps sugar

520 mL milk

4 eggs

8 tbsps oil

Step-by-step explanation:

Multiply each ingredient by 4!

Because the initial recipie provides the amounts for 6, simply divide 24/6 and you'll find that you only need 4x the original recipie.

135g*4 = 540

1 tsp*4 = 4 etc!

Answer:

[D] [tex]\displaystyle \lim_{h \to 0} \frac{[5(x + h)^2 - 2(x + h)] - (5x^2 - 2x)}{h}[/tex]

General Formulas and Concepts:

Calculus

Limits

Derivatives

Definition of a Derivative: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle f(x) = 5x^2 - 2x[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

Answer:

25%

Step-by-step explanation:

400/100•300/x=0.75

1.00-0.75= 0.25

25%

Answer:

25 percent of discount

Step-by-step explanation:

[tex]original_price=400\\final_price=300\\discount=100\\\\\frac{400*percent}{100}=100 =>percent=\frac{100^2}{400}=25[/tex]

Answer:

5:15 or can be simplified to 1:3

Step-by-step explanation:

There are 5 boys out of 15 total students in glee club.

(x + 3)(x − 2) in standard form

x2+x-6

Answer:

the answer is D :))) hope you pass this