A study was done on the batting averages for two baseball players: Hitmore and Bunter. Data were collected over a period of time for baseball parks that are natural and artificial turf. It was found that Hitmore does better overall (.e., has a better batting average). However, for both natural and artificial turf separately, Bunter does better. Which of the following is correct?
This is an example of a negative association between variables.
This is an example of Simpson's Paradox.
"Turf" is a lurking variable in this example
Both (B) and (C) are correct
This situation is mathematically impossible

The question is incomplete. The complete question is :

The population of a certain town was 10,000 in 1990. The rate of change of a population, measured in hundreds of people per year, is modeled by P prime of t equals two-hundred times e to the 0.02t power, where t is measured in years since 1990. Discuss the meaning of the integral from zero to twenty of P prime of t, d t. Calculate the change in population between 1995 and 2000. Do we have enough information to calculate the population in 2020? If so, what is the population in 2020?

Solution :

According to the question,

The rate of change of population is given as :

[tex]$\frac{dP(t)}{dt}=200e^{0.02t}$[/tex]  in 1990.

Now integrating,

[tex]$\int_0^{20}\frac{dP(t)}{dt}dt=\int_0^{20}200e^{0.02t} \ dt$[/tex]

                    [tex]$=\frac{200}{0.02}\left[e^{0.02(20)}-1\right]$[/tex]

                   [tex]$=10,000[e^{0.4}-1]$[/tex]

                    [tex]$=10,000[0.49]$[/tex]

                    =4900

[tex]$\frac{dP(t)}{dt}=200e^{0.02t}$[/tex]

[tex]$\int1.dP(t)=200e^{0.02t}dt$[/tex]

[tex]$P=\frac{200}{0.02}e^{0.02t}$[/tex]

[tex]$P=10,000e^{0.02t}$[/tex]

[tex]$P=P_0e^{kt}$[/tex]

This is initial population.

k is change in population.

So in 1995,

[tex]$P=P_0e^{kt}$[/tex]

   [tex]$=10,000e^{0.02(5)}$[/tex]

   [tex]$=11051$[/tex]

In 2000,

[tex]$P=10,000e^{0.02(10)}$[/tex]

   [tex]=12,214[/tex]

Therefore, the change in the population between 1995 and 2000 = 1,163.

Answer:

-5/16 or -0.3125

Step-by-step explanation:

Answer:

-11/12

Step-by-step explanation:

Fyi you can use the app photo math you just take a pic of the problem and it gives you the answer and explains the steps and it is free.

Answer:

2.5

Step-by-step explanation:

5/8 ÷ 1/4

Division sign changes to multiplication and the reciprocal of the divisior is used to multiply instead :

5/8 * 4/1

= (5*4) / (8*1)

= 20 / 8

= 2.5

Answer:

Newton's law of cooling says that:

T(t) = Tₐ + (T₀ - Tₐ)*e^(k*t)

or:

[tex]\frac{dT}{dt} = -k*(T - T_a)[/tex]

in the differential form.

where:

T is the temperature as a function of time

Tₐ  is the ambient temperature, in this case, 70F

T₀ is the initial temperature of the object, in this case, 150F

k is a constant, and we want to find the value of k.

Then our equation is:

T = 70F + (150F - 70F)*e^(k*t)

Now we also know that after a minute, or 60 seconds, the temperature was 135F

then:

135F = 70F + (150F - 70F)*e^(k*60s)

We can solve this for k:

135F = 70F + 80F*e^(k*60s)

135F - 70F = 80F*e^(k*60s)

65F =  80F*e^(k*60s)

(65/80) = e^(k*60s)

Now we can apply the Ln(x) function to both sides to get:

Ln(65/80) = Ln(e^(k*60s))

Ln(65/80) = k*60s

Ln(65/80)/60s = k = -0.0035 s^-1

Then the differential equation is:

[tex]\frac{dT}{dt} = -0.0035 s^-1*(T - 70F)[/tex]

Answer: Read it to him again, and explain all the steps to him nice and slowly.

Answer:

242 m³ of space is there in the fort.

Step-by-step explanation:

Given that,

The dimensions of first box is 4 meters long, 8 meters wide, and 8 meters high.

The dimensions of the second box is 2 meters long, 7 meters wide, and 1 meter high.

Space left = Volume of first box - volume of second box

= (4)(8)(8) - 2(7)(1)

= 242 m³

So, 242 m³ of space is there in the fort.

Answer:

-1 over 2

Step-by-step explanation:

Answer:

-1/2

Step-by-step explanation:

The line joins (-2, 2) and (0, 1).

Remember that slope equals change in y all divided by the change in x.

Here,

change in y = 1 - 2 =- 1

change in x = 0 -(-2) = 2

Thus, slope =- 1/2

Given:

The ratio of the number of Rs2 coins to the number of Rs5 coins is 1:3.

The value of all the Rs5 coins is Rs45.

To find:

The value of all the Rs2 coins in the box.

Solution:

Let x be the number of Rs2 coins and y be the number of Rs5 coins.

The value of all the Rs5 coins is Rs45.

[tex]5y=45[/tex]

[tex]y=\dfrac{45}{5}[/tex]

[tex]y=9[/tex]

The ratio of the number of Rs2 coins to the number of Rs5 coins is 1:3.

[tex]\dfrac{x}{y}=\dfrac{1}{3}[/tex]

[tex]\dfrac{x}{9}=\dfrac{1}{3}[/tex]

Multiply both sides by 9.

[tex]\dfrac{x}{9}\times 9=\dfrac{1}{3}\times 9[/tex]

[tex]x=3[/tex]

The value of all the Rs2 coins in the box is:

[tex]\text{Required value}=2x[/tex]

[tex]\text{Required value}=2(3)[/tex]

[tex]\text{Required value}=6[/tex]

Therefore, the value of all the Rs. 2 coins in the box is Rs. 6.

9514 1404 393

Answer:

  5

Step-by-step explanation:

The number 5 is a counterexample, as is any number ending in 5.

  5 ÷ 2 = 2 remainder 1

The non-zero remainder indicates 5 is not divisible evenly by two.

Answer:

this probability is 0.68

Step-by-step explanation:

the probability she buys fruit but not a CD is

0.6 × (1 - 0.2) = 0.48

the probability she buys a CD by not fruit is

0.2 × (1 - 0.6) = 0.08

the probability that she buys both is

0.6 × 0.2 = 0.12

the probability that she buys fruit or a CD or both is adding all 3 probabilities :

0.48 + 0.08 + 0.12 = 0.68

Answer:

0

Step-by-step explanation:

If you are looking for the x- intercept image is below

if you are looking for the y- intercept its the same as the x. Image is below

Answer:

5 rows of 4 each

4 rows of 5 each

2 rows of 10 each

10 rows of 2 each

1 row of 20

20 rows of 1

Step-by-step explanation:

Answer:

The agency makes 16110

The agent makes 3222

Step-by-step explanation:

First find the real estate commission

358000 * 4.5%

358000*.045

16110

The agent gets 20 percent of that amount

16110*20%

16110*.2

3222

Answer:

option B : 31.4 cm

Step-by-step explanation:

Given radius , r = 5cm

Circumference = [tex]2 \pi r[/tex]

                       = 2 x 3.14 x 5

                       =10 x 3.14

                       = 31.4 cm

Answer:

b. 31.4

Step-by-step explanation:

The radius of the circle can be plugged into C=(pi)2r. So 5x2= 10 and 10x(pi)= 31.4

Answer:

2b^2

Step-by-step explanation:

according to the question equation is

(a^2 + b^2 ) - (a^2 - b^2)

a^2 + b^2 - a^2 + b^2

plus a square and minus a square gets cancel

b^2 + b^2

since they are like terms they can be added

2b^2

Answer:

2b^2

Step-by-step explanation:

according to the question equation is

(a^2 + b^2 ) - (a^2 - b^2)

a^2 + b^2 - a^2 + b^2

= b^2 + b^2

like terms can be added

+2b^2

Answer:

A

Step-by-step explanation:

Answer:

C

Step-by-step explanation:  

Answer:

I. m = 2401

II. ((n+1) ∆ y)/n = 1/n[(n – y + 2)(n – y) + 1]

Step-by-step explanation:

I. Determination of m

x ∆ y = x² − 2xy + y²

2 ∆ − 5 = √m

2² − 2(2 × –5) + (–5)² = √m

4 – 2(–10) + 25 = √m

4 + 20 + 25 = √m

49 = √m

Take the square of both side

49² = m

2401 = m

m = 2401

II. Simplify ((n+1) ∆ y)/n

We'll begin by obtaining (n+1) ∆ y. This can be obtained as follow:

x ∆ y = x² − 2xy + y²

(n+1) ∆ y = (n+1)² – 2(n+1)y + y²

(n+1) ∆ y = n² + 2n + 1 – 2ny – 2y + y²

(n+1) ∆ y = n² + 2n – 2ny – 2y + y² + 1

(n+1) ∆ y = n² – 2ny + y² + 2n – 2y + 1

(n+1) ∆ y = n² – ny – ny + y² + 2n – 2y + 1

(n+1) ∆ y = n(n – y) – y(n – y) + 2(n – y) + 1

(n+1) ∆ y = (n – y + 2)(n – y) + 1

((n+1) ∆ y)/n = [(n – y + 2)(n – y) + 1] / n

((n+1) ∆ y)/n = 1/n[(n – y + 2)(n – y) + 1]

Answer:

Thw sum of 1/4 and 1/2 is 3/4

Step-by-step explanation:

You have to put them in common like terms so

1/4 + 1/2 = ?

1/4 + 2/4 = 3/4

1/4 + 1/2

(1 + 1*2)/4

3/4

I hope it's help you...

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Answer:

[tex]F^{-1} (x) = 2x + 12[/tex]

Step-by-step explanation:

Let's assume F(x) = y, then

[tex]y = \frac{1}{2} x - 6[/tex]

Let us solve the equation for x.

[tex]y + 6 = \frac{1}{2} x[/tex]

[tex]2y + 12 = x[/tex]

Next, replace y with x and also replace x with F⁻¹(x)

Answer: [tex]F^{-1} (x) = 2x + 12[/tex]

Answer:

[tex]h(x) = \frac {3}{2}x + 1 \\ { \tt{let \: the \: inverse \: be \: { \bold{m}}}} \\ { \tt{m = \frac{1}{ \frac{3}{2}x + 1 } }} \\ \\ { \tt{m = \frac{2}{3x + 2} }} \\ \\ { \tt{m(3x + 2) = 2}} \\ \\ { \tt{3x + 2 = \frac{2}{m} }} \\ \\ { \tt{x = \frac{2 - 2m}{3m} }} \\ \\ { \tt{x = \frac{2}{3m}(1 - m) }} \\ \\ { \bf{h {}^{ - 1} (x) = \frac{2}{3x}(1 - x) }}[/tex]

Answer:

d = 52°

Step-by-step explanation:

The two sides with little marks are congruent.

That means that the opposite angles are congruent.

One angle measures 76°.

The other to angles measure d each.

d + d + 76 = 180

2d + 76 = 180

2d = 104

d = 52

Answer:

16

Step-by-step explanation:

baámmáy tính  

Step-by-step explanation:

Using an online calculator, I was able to find that one pattern is

[tex]a_{n} = a_{n-1} + 14 * 3^{n-1}[/tex] . Finding a recursive sequence is generally based on guess and check, so there isn't much explanation to obtaining one