The harmonic mean of two real numbers x and y equals 2xy/(x + y). By computing the harmonic and geometric means of different pairs of positive real numbers, formulate a conjecture about their relative sizes and prove your conjecture.

Answer:

1)  2/20 x 200 = 1/10 x 200 = 20

2) 3/20 x 200 = 30

3) 4/20 x 200 = 1/5 x 200 = 40

4) 5/20 x 200 = 1/4 x 200 = 50

5) 18/20 = 9/10 x 200 = 180

Answer:

17.

Step-by-step explanation:

The differences form an arithmetic sequence 3, 5, 7, 9,,11.

The missing number  is 10 + 7 = 17.

This is a quadratic sequence.

The nth term = n^2 + 1.

Thus the 4th term = 4^2 + 1 = 17.

Answer:

The width of the rectangle lies between 12 and 20.

Step-by-step explanation:

Let the width of the rectangle is w.

length of the rectangle,

L = 8 w + 20

116 < L < 180

So,

116 < 8 w + 20 < 180

96 < 8 w < 160

12 < w < 20

So, the width of the rectangle lies between 12 and 20.

Answer:

About 135.

Step-by-step explanation:

As the sample is random the number of monkeys likely to be in the zoo

=  (22/65) * 400

= 135.38

Answer:

87 gallons

Step-by-step explanation:

5 gallons: 3 weeks = x gallons: 52 weeks

5/3 = x/52

3x = 260

x= 86.6, about 87 gallons

9514 1404 393

Answer:

  C.  -2.00 m/sec

Step-by-step explanation:

The average velocity on the interval [a, b] is found by ...

  m = (s(b) -s(a))/(b -a)

One end of the interval remains constant here, so we can define 'd' so that the interval is [4, 4+d]. Then the average velocity is ...

  m = (s(4 +d) -s(4))/((4 +d) -4)

  m = (s(4+d) -s(4))/d

The attached table shows the average velocity values on the intervals required by the problem statement. Respectively, they are ...

  -1.5 m/s, -1.7 m/s, -1.9 m/s, -1.99 m/s, 2.01 m/s, 2.1 m/s, 2.3 m/s, 2.5 m/s

We expect the instantaneous velocity at d=0 to be the average of the values at d=-0.01 and d=+0.01. We estimate the instantaneous velocity at t=4 seconds to be -2.00 m/s.

Answer:

90 kilometers

Step-by-step explanation:

https://www.bing.com/search?q=kilometers+are+there+in+9000000cm

Answer:

4%

Step-by-step explanation:

264 interest/3 years=88 interest/year

principal x interest rate =interest/year

2200 x interest rate =88

interest rate =88/2200

interest rate =.04 or 4%

Answer:

[tex]A=379.94\ m^2[/tex]

Step-by-step explanation:

Given that,

The radius of a circl is 11 m

We need to find the area of the circle. The forcemula for the area of a crcle is given by :

[tex]A=\pi r^2[/tex]

Put all the values,

[tex]A=3.14\cdot11^{2}\\A= 379.94\ m^2[/tex]

So, the area of the circle is equal to [tex]379.94\ m^2[/tex].

Answer:94.985 m 2

Step-by-step explanation:

the answer is b. insurance

Answer:

the slopes are different, and the y-intercepts are also different

Step-by-step explanation:

We can rewrite the equations given in slope-intercept to easily determine the slope (m) and the y-intercept (b). Slope-intercept equation is y = mx + b

Let's rewrite each equation:

✔️5x + 2y = 2

Subtract 5x from each side

2y = -5x + 2

Divide both sides by 2

y = -5x/2 + 2/2

y = -⁵/2(x) + 1

The slope (m) = -⁵/2

y-intercept (b) = 1

✔️3x - 3y = 18

Subtract 3x from each side

-3y = -3x + 18

Divide both sides by -3

y = -3x/-3 + 18/-3

y = x - 6

Slope (m) = 1

y-intercept (b) = -6

✅Therefore, the slopes are different and the y-intercepts are also different

Answer:

a.) 15 feet

b.) 3.25 seconds

c.) 17.1125 feet

d.) 12.5 seconds

Step-by-step explanation:

a

This is just asking for the y intercept

to get this just do h(0)= 15

b

This is asking for the x value of the vertex

solve that through -b/2a

-1.3/(2*-.2)= 3.25

c

This is asking for the y value of the vertex

to solve this plug in the x value from b

-.2*3.25²+1.3*3.25+15= 17.1125

d

This is asking for an x intercept

using the quadratic formula...

[tex]\frac{-b(+-)\sqrt{b^2-4*a*c}}{2a}=\frac{-1.3(+-)\sqrt{1.3^2-4*-.2*15}}{2*-.2}= -6, 12.5[/tex]

*note the (+-) before the radical is ± *

logic will tell us that a negative x intercept doesn't make any sense so we only take the positive value, 12.5

Answer:

The null (H[tex]_{0}[/tex]) and alternative (H[tex]_{1}[/tex]) hypotheses can be stated as follows:

H[tex]_{0}[/tex]:  μ[tex]_{1}[/tex] = μ[tex]_{2}[/tex].

H[tex]_{1}[/tex]: μ[tex]_{1}[/tex] > μ[tex]_{2}[/tex].

Step-by-step explanation:

In the question, the given assertion is that carpeted rooms have more bacteria than uncarpeted rooms, i.e. μ[tex]_{1}[/tex] > μ[tex]_{2}[/tex].

The assertion made in the question can either be the null hypothesis (H[tex]_{0}[/tex]) or the alternate hypothesis (H[tex]_{1}[/tex]). An equality must be present in the null hypothesis. The alternative hypothesis expresses the exact opposite of the null hypothesis if the claim is the null hypothesis.

Therefore, the null (H[tex]_{0}[/tex]) and alternative (H[tex]_{1}[/tex]) hypotheses can be stated as follows:

H[tex]_{0}[/tex]:  μ[tex]_{1}[/tex] = μ[tex]_{2}[/tex].

H[tex]_{1}[/tex]: μ[tex]_{1}[/tex] > μ[tex]_{2}[/tex].

Answer:

153.86.

Step-by-step explanation:

Use the formula pi times radius squared.

Answer and Step-by-step explanation:

Solve for x.

First, we divide both sides of the equation by 2.

2(8 - 2x) = 7 - x

Distribute the 2.

16 - 4x = 7 - x

Add 4x to and subtract 7 from both sides of the equation.

9 = 3x

Divide by 3 to both sides of the equation.

x = 3 <-- This is the answer.

#teamtrees #PAW (Plant And Water)

Answer:

x = 3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

4(8 - 2x) = 2(7 - x)

Step 2: Solve for x

Answer:

bacteria 1

Step-by-step explanation:

i got it right

Answer:

(2,1)

Step-by-step explanation:

-3x + 7 = -2x + 5

x = 2

y = -6 + 7

y = 1

Answer:

(2,1)

Step-by-step explanation:

Remark

One thing you need to remind yourself of: The y value in both equations must be the same.

That means that the two right hand values are

-3x + 7 = - 2x + 5         Subtract 5 from both sides.

      -5              -5

-3x + 2 = - 2x               Add 3x to both sides

+3x          +3x

       2 = x

Now use one of the equations to solve for y

y = -2x + 5

y = -2(2) + 5

y = - 4 + 5

y = 1

We should check this by graphing it. Notice the two graphs do cross at (2,1) just as predicted.

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the right trianglea are not given. The general explanation is as follows.

Using Pythagoras Theorem, we have:

a² = b² + c²

Where:

a => hypotenuse

Assume that the opposite and the adjacent sides are given as 3 and 4, respectively.

The hypotension becomes

a² = 3² + 4²

a² = 9 + 16.

a² = 25

Take square roots.

a = 5

If any of the other side lengths is missing; you make that side the subject and then solve.

Answer:

D

Step-by-step explanation:

The radius of a circle refers to a segment connecting the center of the circle to the circumference of the circle. This can be seen in selection D), as a segment connects the center of the circle (O) to the circumference or outer edge of the circle.

Answer:

Buses - 43 people

Vans - 12 people

Answer:

x=2

Step-by-step explanation:

the sides are proportional due the angles being equal

since the hypotonuse is 5 on the bigger one and 2.5 on the small one we can infer there is a ×2 difference

so 4÷2=x

x=2

The Probability is 1/2 or .5, .5 rounded to the nearest tenth would be irregular because .5 is already in the tenth place but according to the law of rounding since ut is five it would be rounded up giving the whole number 1

Answer:

105

Step-by-step explanation:

So, we know the formula is:

D=rt or D=r*t

We only need 2 of the 3 sets of values given in the table, one to find our answer, and the other to double check our answer.

Here are the two sets we can look at:

t=2, d=210

t=3, d=315

Lets plug these in and solve:

210=r*2

Divide both sides by 2 to get r alone:

105=r

Now lets check if this is true by pluggin in 105 for r in the second set, and seeing if it works:

D=r*t

315=105*3

=

315=315

So 105 is our answer.

Hope this helps!

Answer:

A (-1,-10) ; A (-1,14)

Step-by-step explanation:

[tex]\sqrt{(-1-4)^2 + (y-2)^2} = 13 \\ 25 + y^2 + 4 -4y = 169[/tex]

y^2 -4y - 140 = 0

Δ/4 = 4 + 140 = 144

y1 = 2 + 12 = 14

y2 = 2 -12= -10

Answer:

I'd use A = πr^2

The area is 28.3 if we're using 3.14 as pi (rounded to the nearest tenth)