A study published in 1993 found that babies born at different times of the year may develop the ability to crawl at different ages! The author of the study suggested that these differences may be related to the temperature at the time the infant is 6 months old. (Benson and Janette, Infant Behavior and Development [1993]. The study found that 32 babies born in January crawled at an average age of 29.84 weeks, with a standard deviation of 7.08 weeks. Among 21 July babies, crawling ages averaged 33.64 weeks, with a standard deviation of 6.91 weeks. Is this difference significant?

Answers

Answer 1
Answer:

Answer:

t=\frac{(29.84-33.64)-0}{\sqrt{(7.08^2)/(32)+(6.91^2)/(21)}}}=-1.939  

p_v =2*P(t_(51)<-1.939)=0.0580  

Comparing the p value with the significance assumed \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and the difference between the two groups is NOT significantly different at 1% of significance.  

Step-by-step explanation:

Data given

\bar X_(1)=29.84 represent the mean for sample January

\bar X_(2)=33.64 represent the mean for sample July

s_(1)=7.08 represent the sample standard deviation for 1  

s_(2)=6.91 represent the sample standard deviation for 2  

n_(1)=32 sample size for the group 2  

n_(2)=21 sample size for the group 2  

\alpha=0.01 Significance level provided

t would represent the statistic (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the difference in the population means, the system of hypothesis would be:  

Null hypothesis:\mu_(1)-\mu_(2)=0  

Alternative hypothesis:\mu_(1) - \mu_(2)\neq 0  

We don't have the population standard deviation's, so for this case is better apply a t test to compare means, and the statistic is given by:  

t=\frac{(\bar X_(1)-\bar X_(2))-\Delta}{\sqrt{(\sigma^2_(1))/(n_(1))+(\sigma^2_(2))/(n_(2))}} (1)  

And the degrees of freedom are given by df=n_1 +n_2 -2=32+21-2=51  

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.  

With the info given we can replace in formula (1) like this:  

t=\frac{(29.84-33.64)-0}{\sqrt{(7.08^2)/(32)+(6.91^2)/(21)}}}=-1.939  

P value  

Since is a bilateral test the p value would be:  

p_v =2*P(t_(51)<-1.939)=0.0580  

Comparing the p value with the significance assumed \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and the difference between the two groups is NOT significantly different at 1% of significance.  


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The following are the ages (years) of 5 people in a room: 25, 18, 17, 13, 24 A person enters the room. The mean age of the 6 people is now 22. What is the age of the person who entered the room?

Answers

Answer:

See Below:

Step-by-step explanation:

Average is take by adding all the terms together and dividing by the number of terms. In this case it terms is people in the room.

22= (25+18+17+13+24+x)/6

Where 22 is the average age. The numerator is all the known ages added together, plus x which is the age of the person who just entered. Divided by 6 because you are finding the average age of 6 people.

22 = (25+18+17+13+24+x)/6     Multiply both sides by 6

132= 97+ x  Subtract 97 from both sides.

35 = x

The person who just entered the room is 35 years old.

Final answer:

To solve this, we first find the total age of the original five people, then the total age of all six with the given mean age. By subtracting these, we find that the age of the person who entered is 35 years old.

Explanation:

This problem can be solved using simple arithmetic. First, we calculate the total age of the first 5 people, which is 25 + 18 + 17 + 13 + 24 = 97 years. Then, we need to determine the total age of all 6 people. We're told the mean (average) age of these 6 people is 22. We find the total by multiplying the mean by the number of people, so 22 * 6 = 132 years. Finally, to find the age of the person who entered the room, we subtract the total age of the first 5 people from this new total, i.e. 132 - 97 = 35 years. So, the person who entered the room is 35 years old.

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The tax on a property with an assessed value of $90,000 is $1,350. Find the tax on a property with anassessed value of $140,000.
a. $1500.00
b. $150.00
c. $2100.00
d. $210.00
e. $750.00

Answers

Answer:

0.015 or 1.5% tax

Step-by-step explanation:

90000x0.015 = 1350

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A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides.Suppose the paper is 7"-wide by 9"-long.
a. Estimate the maximum volume for this box?
b. What cutout length produces the maximum volume?

Answers

To answer this question it is necessary to find the volume of the box as a function of "x", and apply the concepts of a maximum of a function.

The solution is:

a) V (max) = 36.6 in³

b) x = 1.3 in

The volume of a cube is:

V(c) = w×L×h  ( in³)

In this case, cutting the length  "x" from each side, means:

wide of the box    ( w - 2×x )   equal to  ( 7 - 2×x )

Length of the box ( L - 2×x )   equal to  ( 9 - 2×x )

The height  is  x

Then the volume of the box,  as a function of x is:

V(x) = ( 7 - 2×x ) × ( 9 -2×x ) × x

V(x) = ( 63 - 14×x - 18×x + 4×x²)×x

V(x) = 4×x³ - 32×x² + 63×x

Tacking derivatives,  on both sides of the equation

V´(x) = 12×x² - 64 ×x + 63

If   V´(x) = 0      then      12×x² - 64 ×x + 63 = 0

This expression is a second-degree equation, solving for x

x₁,₂ = [ 64 ± √ (64)² - 4×12*63

x₁ =  ( 64 + 32.74 )/ 24

x₁ = 4.03     this value  will bring us an unfeasible solution,  since it is not possible to cut 2×4 in from a piece of paper of 7 in ( therefore we dismiss that value)

x₂ = ( 64 - 32.74)/24

x₂ = 1.30 in

The  maximum volume of the box is:

V(max) = ( 7 - 2.60) × ( 9 - 2.60)×1.3

V(max) = 4.4 × 6.4 × 1.3

V(max) = 36.60 in³

To chek for maximum value of V when x = 1.3

we find the second derivative of V  V´´,  and substitute the value of x = 1.3,    if the relation is smaller than 0,  we have a maximum value of V

V´´(x) = 24×x - 64 for x = 1.3

V´´(x) = 24× 1.3 - 64            ⇒   V´´(x) < 0

Then the value  x = 1.3 will bring maximum value for V

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Final answer:

The maximum volume of the box that can be formed is approximately 17.1875 cubic inches. The cutout length that would result in this maximum volume is approximately 1.25 inches.

Explanation:

To solve this problem, we will use optimization in calculus. Let's denote the length of the square cutout as 'x'. When you cut out an x by x square from each corner and fold up the sides, the box will have dimensions:

  • Length: 9 inches (the original length) - 2x (the removed parts)
  • Width: 7 inches (the original width) - 2x
  • Height: x inches (the height is the cutout's length)

So the volume V of the box can be given by the equation: V = x(9-2x)(7-2x). We want to maximize this volume.

To find the maximum, differentiate V with respect to x, equate to zero and solve for x. V' = (9-2x)(7-2x) + x(-2)(7-2x) + x(9-2x)(-2) = 0. We obtain x=1.25 inches, but we need to verify whether this value gives us a maximum. Second differentiation, V'' = -12 is less than zero for these dimensions so the V is maximum.

a. So, when we solve, the maximum volume will be approximately 17.1875 cubic inches.

b. The cutout length that would produce the maximum volume is therefore about 1.25 inches.

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Can someone help me out this is hard

Answers

Answer:

a function needs inputs and outputs so just fill in anything that doesn't directly cooralate to itself

Step-by-step explanation:

Answer:

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Answers

Horizontal translations
 Suppose that h> 0
 To graph y = f (x + h), move the graph of h units to the left.
 We have then:
 G (x) = f (x + h)
 G (x) = (x + 5) ^ 2
 Answer:
 
The graph of G (x) is given by:
 
G (x) = (x + 5) ^ 2
 
option D
From the graphs we can observe that G(x) is 5 units to the left of F(x). 

This means a horizontal translation of 5 units to the left of F(x) will result in G(x). Such a translation can be obtained from adding 5 to each x in the equation.

So,

G(x) = F(x+5)

F(x) = (x+5)²

So the correct answer is option D

Solve the system of equations. \begin{aligned} & -9x+4y = 6 \\\\ & 9x+5y=-33 \end{aligned} ​ −9x+4y=6 9x+5y=−33 ​

Answers

Answer:

x = -2

y = -3

Step-by-step explanation:

We can use either substitution or elimination for this problem. I will use elimination to solve this problem:

Step 1: Eliminate x by adding the 2 equations together

9y = -27

y = -3

Step 2: Plug in y into one of the original equations to get x

-9x + 4(-3) = 6

-9x -12 = 6

-9x = 18

x = 2

And we have our final answers!