MATHEMATICS HIGH SCHOOL

Identify the 27th term of an arithmetic sequence where a1 = 38 and a17 = -74. -20.5
-151
-22.75
-144

Answers

Answer 1
Answer: Arithmetic sequence:
an=a1+(n-1)d
a_(17)= a_(1)+16d -74=38 + 16d 16d=-74-38 16d=-112
d=-112/16=-7
a_(27)=a_(1) + 26d=38+26*(-7)=38-182=-144
Answer: D)-144
Answer 2
Answer:

Answer:

d) -144

Step-by-step explanation:

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There are 2,100 bacteria in a circular petri dish. The dish has a radius of 40 millimeters. What is the approximate population density? (Use 3.14 for π)

Answers

A petri dish is simply a circle; thus, we use the formula of the area of the circle which is πr^2. 
Given r = 40 mm
A = π(40)^2 = 5026.55 sq. mm

Population density = bacteria count / area
PD = 2,100 / 5026.55
PD = 0.417782 bacteria / mm sq.

Therefore, the answer is approximately 0.418 bacteria per square millimeter.
Determine the area of the circular petri dish through the equation, A = πr^2. Substituting the radius to the equation and solving for area gives, 5024 mm^2. The population density is obtained by dividing the population with the calculated area. Thus, the population density is approximately 0.418 bacteria per mm^2. 

In a hydraulic system, piston 1 has a surface area of 100 cm2, and piston 2 has a surface area of 900 cm2. Piston 1 exerts a pressure of 10 Pa on the fluid in the hydraulic lift.What is the fluid pressure on piston 2?

Answers

By hydraulic principles the pressures are equal.

Then pressure on piston 2 = pressure on piston = 10 Pa.

That is what permits to apply a low force on the surface of the piston with the smaller area and get a bigger force on sureface of the piston with the greater area.

Answer:10 Pa

Step-by-step explanation: gradpoint

What is the answer for 56% of 80

Answers

56% of 80 56/100 X 80/1= 224/5 = 44 4/5 or 44.8
0.56 x 80 = 44.8

(56% divided by 100 to get the percentage and will work for any percentage

If a function f ( x ) has values f ( 4 ) = 6 and f ( 8 ) = 18, use what you have learned about function patterns to find f ( 16 ) = if f ( x ) is: a.) Linear function: f ( 16 ) = b.) Power function: f ( 16 ) = c.) Exponential function: f ( 16 ) = d.) Logarithmic function: f ( 16 ) =

Answers

Answer:

a) f(16) = 42

b) f(16) = 54

c) f(16) = 162

d) f(16) = 30

Step-by-step explanation:

a) y = mx + b ∧ m = (f(8) - f(4))/(8-4) ⇒ m = (18 - 6)/(8 - 4) = 3

b = y - mx = 6 - 3(4) = 6 - 12 = - 6

f(16) = 3(16) - 6 = 42

b) y = kxⁿ ∧ f(4) = 6 = k4ⁿ ∧ f(8) = 18 = k8ⁿ ⇒ 18/6 = (k8ⁿ)/(k4ⁿ) ⇒ 3 = 2ⁿ

n = ㏑(3) / ㏑(2) ⇒ k = y/xⁿ ⇒ k = 6/4ⁿ = 2/3

f(16) = 2/3 × 16ⁿ = 54

c) y = aeᵇˣ ∧ f(4) = 6 = aeᵇ⁴ ∧ f(8) = 18 = aeᵇ⁸ ⇒ 18/6 = (aeᵇ⁸)/(aeᵇ⁴) ⇒ 3 = e⁴ᵇ

b = ㏑(3/4) ∧ a = y / eᵇˣ ⇒ a = 6 / e⁴ᵇ = 2

f(16) = 2eᵇ¹⁶ = 162

d) y = a㏑(bx) ∧ f(4) = 6 = a㏑(b4) ∧ f(8) = 18 = a㏑(b8)

⇒ 18 - 6 = a㏑(b8) - a㏑(b4) ⇒ 12 = a㏑(8b/4b) ⇒ a = 12 / ㏑(2)

f(4) = 6 = a㏑(4b) ⇒ b = (√2)/4

f(16) = a㏑(b16) = 30

7) What is a check? What is a money order? 8) When someone writes a check, where is the money coming from?
9) When someone pays with a money order, where is the money coming from?
10) Do you think it is more secure to have someone pay you with a check or a money order? Explain.
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Answers

7) Check - a piece of paper that has a certain amount of money deposited or withdrawn from a bank and deposited to a certain person or owner.Money Order - a receipt that shows that the owner (payee) receives and certain amount of money and is therefore payed that amount.8) When someon writes a check, the money usually comes from their bank account.9) When someone pays with a money order, the money usually comes from from a financial bureau.10) A check is better because, checks can be deposited and withdrawn, but money orders are usually money, so there is no proof. Maybe someone might not pay money.12) Find the unit rate -Lawn moving = 300/2 = $150 per hourLandscaping = 2800/35 = $80 per hourLawn moving is the better job, because Amy gets payed more.

Point P has coordinates (2,3). Point Q is symmetric to point P with respect to the line x = 4. What are the coordinates of point Q. Im wondering how you solve this. I think it's (3,6) A. (2,5)
B. ( 5,3)
C. (3,6)
D. (6,3

Answers

You are given the first point (2, 3) and a line x = 4. If you go ahead and graph these, it makes it a little more clear when they say that point p is symmetric with point Q with respect to the line x = 4.

Line x = 4 is the line of symmetry, so point Q is reflected across it. Point p has an x value of 2 (2 away from the line of symmetry, so point Q's x value has to be 2 away on the other side... 6. The y value is unchanged so your point is

D. (6, 3)
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