Suppose you are climbing a hill whose shape is given by the equation z = 1600 − 0.005x2 − 0.01y2, where x, y, and z are measured in meters, and you are standing at a point with coordinates (120, 80, 1464). The positive x-axis points east and the positive y-axis points north. (a) If you walk due south, will you start to ascend or descend?

Answer:

A. This statement A is false.

B. This statement A is false.

C. This statement is true .

Step-by-step explanation:

Determine which of the following statements is true.

From the statements we are being given , we are to determine if the statements are valid to be true or invalid to be false.

SO;

A: If V is a 6-dimensional vector space, then any set of exactly 6 elements in V is automatically a basis for V

This statement A is false.

This is because any set of exactly 6 elements in V is linearly independent vectors of V . Hence, it can't be automatically a basis for V

B. If there exists a set that spans V, then dim V = 3

The statement B is false.

If there exists a set , let say [tex]v_1 ...v_3[/tex], then any set of n vector (i.e number of elements forms the basis of V)  spans V. ∴ dim V < 3

C. If H is a subspace of a finite-dimensional vector space V  then dim H ≤ dim V is a correct option.

This statement is true .

We all know that in a given vector space there is always a basis, it is equally important to understand that there is a cardinality for every basis that exist ,hence the dimension of a vector space is uniquely defined.

SO,

If  H is a subspace of a finite-dimensional vector space V  then dim H ≤ dim V is a correct option.

Answer:

The answer is option A.

Step-by-step explanation:

Using the properties of logarithms

that's

[tex] log(x) - log(y) = log( \frac{x}{y} ) [/tex]

log 2 - log 14 is

[tex] log(2) - log(14) = log( \frac{2}{14} ) [/tex]

Simplify

We have the final answer as

[tex] log( \frac{1}{7} ) [/tex]

Hope this helps you

Answer:

log ( 1/7)

Step-by-step explanation:

log2-log14

We know that log ( a/b) = log a - log b

log (2 /14)

log ( 1/7)

Answer:

x = 30

Step-by-step explanation:

1/2(x+6) = 18

Expand brackets or use distributive law.

1/2(x) + 1/2(6) = 18

1/2x + 6/2 = 18

1/2x + 3 = 18

Subtract 3 on both sides.

1/2x + 3 - 3 = 18 - 3

1/2x = 15

Multiply both sides by 2.

(2)1/2x = (2)15

x = 30

Answer:

30

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

Answer:

Let E be the event that the first marble selected is green. Let F be the event that the second marble selected is green. A box contains 20 blue marbles, 16 green marbles and 14 red marbles P(F/E)=15/49 because if the first marble selected is green there are 49 in total and 15 are green. I think this is it.

Step-by-step explanation:

Answer:

the difference between the estimator and the population parameter grows smaller as the sample size grows larger.

Step-by-step explanation:

In Statistics, an estimator is a statistical value or quantity, which is used to estimate a parameter.

Generally, parameters are the determinants of the probability distribution. Thus, to determine a normal distribution we would use the parameters, mean and variance of the population.

An estimator is said to be consistent if the difference between the estimator and the population parameter grows smaller as the sample size grows larger. This simply means that, for an estimator to be consistent it must have both a small bias and small variance.

Also, note that the bias of an estimator (b) that estimates a parameter (p) is given by; [tex]E(b) - p[\tex]

Hence, an unbiased estimator is an estimator that has an expected value that is equal to the parameter i.e the value of its bias is equal to zero (0).

A sample variance is an unbiased estimator of the population variance while the sample mean is an unbiased estimator of the population mean.

Generally, a consistent estimator in statistics is one which gives values that are close enough to the exact value in a population.

Answer:

The option are incorrect because as its slope is only 5/7 the answer will never come like that.

Step-by-step explanation:

Here,

Given,

The dlope of a line is 5/7 and (6,2) is a point.

By one point formulae,

(y-y1)= m (x-x1).

or, (y-2)=5/7(x-1)

or, y = 5/7x -5/7+2

taking lcm of -5/7 and 2. we get,

or, y= 5/7 x -5+7/7

Therefore, the equation is y = 5/7 x -2/7.

Hope it helps..

Answer:

36y² - 1

Factorize

We have the final answer as

[tex](y - \frac{1}{6} )(36y + 6)[/tex]

Hope this helps you

Answer: It will  take you about 61 years for you to reach your goal.

Step-by-step explanation:

We will represent this situation by an exponential function. So if you earn 5% yearly then we could represent it by 1.05.So in exponential function we need to find the initial value and the common difference and in this case the common difference is 1.05 and the initial value or amount is 50,000 dollars.

We could represent the whole situation by the equation.

y= [tex]50,000(1.05)^{x}[/tex]  where x is the number of years. so if you aspire to have 1,000,000 in some years then we will put in 1 million dollars for y and solve for x.

1,000,000 = 50,000(1.05)^x   divide both sides by 50,000

20 = (1.05)^x

x= 61.40

Answer:

500km

Step-by-step explanation:

add all the proportions and then divide by 3. with conversion.

Answer:

a

   [tex]R =13[/tex]

b

  [tex]\= x =8.9[/tex]

c

 [tex]var(x) = 16.57[/tex]

d

 [tex]\sigma = 4.1[/tex]

Step-by-step explanation:

From the question we are given a data set  

      2​, 10​, 15​, 4​, 11​, 10​, 15​, 10​, 2​, 10

     The sample size is  n  = 10

 The range is  

         [tex]R = maxNum - MinNum[/tex]

Where maxNum  is the maximum number on the data set  which is 15

 and  MinNum  is the minimum  number on the data set  which is  2

   So

           [tex]R = 15 - 2[/tex]

           [tex]R =13[/tex]

The mean is mathematically represented as

          [tex]\= x = \frac{\sum x_i}{N}[/tex]

substituting values

          [tex]\= x = \frac{2 + 10 + 15 + 4 + 11 + 10 + 15 + 10 + 2 + 10 }{10}[/tex]

         [tex]\= x =8.9[/tex]

The variance is mathematically evaluated as

        [tex]var(x) = \frac{\sum (x - \= x)^2}{N}[/tex]

substituting values

      [tex]var(x) = \frac{(2 - 8.9 )^2 + (10 - 8.9 )^2 + (15 - 8.9 )^2 +(4 - 8.9 )^2 +(11 - 8.9 )^2 +(10 - 8.9 )^2 +(15 - 8.9 )^2 +(10 - 8.9 )^2 +} {10}[/tex]                    [tex]\frac{(2 - 8.9 )^2 +(10 - 8.9 )^2 }{10}[/tex]

[tex]var(x) = 16.57[/tex]

The standard deviation is  [tex]\sigma = \sqrt{var(x)}[/tex]

substituting values

         [tex]\sigma = \sqrt{16.57}[/tex]

        [tex]\sigma = 4.1[/tex]

Answer:

The volume of the solid is: [tex]\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}[/tex]

Step-by-step explanation:

GIven that :

[tex]y = 2 + sec \ x , -\dfrac{\pi}{3} \leq x \leq \dfrac{\pi}{3} \\ \\ y = 4\\ \\ about \ y \ = 2[/tex]

This implies that the distance between the x-axis and the axis of the rotation = 2 units

The distance between the x-axis and the inner ring is r = (2+sec x) -2

Let R be the outer radius and r be the inner radius

By integration; the volume of the of the solid  can be calculated as follows:

[tex]V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(4-2)^2 - (2+ sec \ x -2)^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(2)^2 - (sec \ x )^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [4 - sec^2 \ x ]dx[/tex]

[tex]V = \pi [4x - tan \ x]^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) - 4(-\dfrac{\pi}{3})+ tan (-\dfrac{\pi}{3})] \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) + 4(\dfrac{\pi}{3})- tan (\dfrac{\pi}{3})] \\ \\ \\ V = \pi [8(\dfrac{\pi}{3}) - 2 \ tan (\dfrac{\pi}{3}) ][/tex]

[tex]\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}[/tex]

Answer:

Hello!! :) The answer to your question is 13,728

Steps will be below.

Step-by-step explanation:

So we will subtract 22,403 and 8,675.

When we do that we will get 13,728

To check your answer we have to do the opposite of subtracting which will be adding.

This is how we check our work: the answer we got was 13,728...we have to take that answer and add it to 8,675 which will give us 22,403

(Both of the numbers are from the question)

At the bottom I attached a picture of how I did the subtracting and how I checked my work.

Sorry for my handwriting......if you can’t understand my handwriting, I attached another picture which is more clearer.

ANSWER TO YOUR QUESTION: 13,728

Brainliest would be appreciated! Thank you :3

Hope this helps! :)

Answer:

The answer is 13,728

Step-by-step explanation:

Check your work with addition.

Answer:

A ) i) X control chart : upper limit = 50.475, lower limit = 49.825

    ii) R control chart : upper limit =  1.191, lower limit = 0

Step-by-step explanation:

A) Finding the control limits

grand sample mean = 1253.75 / 25 = 50.15

mean range = 14.08 / 25 = 0.5632

Based on  X control CHART

The upper control limit ( UCL ) =

grand sample mean + A2* mean range ) = 50.15 + 0.577(0.5632) = 50.475

The lower control limit (LCL)=

grand sample mean - A2 *  mean range = 50.15 - 0.577(0.5632) = 49.825

Based on  R control charts

The upper limit = D4 * mean range = 2.114 * 0.5632 = 1.191

The lower control limit = D3 * mean range = 0 * 0.5632 = 0  

B) estimate the process mean and standard deviation

estimated process mean = 50.15 = grand sample mean

standard deviation = mean range / d2  = 0.5632 / 2.326 = 0.2421

note d2 is obtained from control table

Answer:

We can assume that the decline in the population is an exponential decay.

An exponential decay can be written as:

P(t) = A*b^t

Where A is the initial population, b is the base and t is the variable, in this case, number of hours.

We know that: A = 800,000.

P(t) = 800,000*b^t

And we know that after 6 hours, the popuation was 500,000:

p(6h) = 500,000 = 800,000*b^6

then we have that:

b^6 = 500,000/800,000 = 5/8

b = (5/8)^(1/6) = 0.925

Then our equation is:

P(t) = 800,000*0.925^t

Now, the population after 24 hours will be:

P(24) = 800,000*0.925^24 = 123,166

Answer:

122,070 bacteria.

Step-by-step explanation:AA0ktA=500,000=800,000=?=6hours=A0ekt

Substitute the values in the formula.

500,000=800,000ek⋅6

Solve for k. Divide each side by 800,000.

58=e6k

Take the natural log of each side.

ln58=lne6k

Use the power property.

ln58=6klne

Simplify.

ln58=6k

Divide each side by 6.

ln586=k

Approximate the answer.

k≈−0.078

We use this rate of growth to predict the number of bacteria there will be in 24 hours.

AA0ktA=?=800,000=ln586=24hours=A0ekt

Substitute in the values.

A=800,000eln586⋅24

Evaluate.

A≈122,070.31

At this rate of decay, researchers can expect 122,070 bacteria.

Answer: a) 0.8708, b) 5714, c) 0.000, d) 0.3830

Step-by-step explanation:

(a)

To find P(Z>-1.13):

Since Z is negative, it lies on left hand side of mid value.

Table of Area Under the Standard Normal Curve gives area = 0.3708

So,

P(Z>-1.13) = 0.5 + 0.3708 = 0.8708

(b)

To find P(Z<0.18):

Since Z is positive, it lies on right hand side of mid value.

Table of Area Under the Standard Normal Curve gives area = 0.0714

So,

P(Z<0.18) = 0.5 + 0.0714 = 0.5714

(c)

To find P(Z>8):

Since Z is positive, it lies on right hand side of mid value.

Table of Area Under the Standard Normal Curve gives area = 0.5 nearly

So,

P(Z>8) = 0.5 - 0.5 nearly = 0.0000  

(d)

To find P(| Z | < 0.5)

that is

To find P(-0.5 < Z < 0.5):

Case 1: For Z from - 0.5 to mid value:

Table of Area Under the Standard Normal Curve gives area = 0.1915

Case 2: For Z from mid value to 0.5:

Table of Area Under the Standard Normal Curve gives area = 0.1915

So,

P(| Z | < 0.5) = 2 * 0.1915 = 0.3830

The Probability can be determine using z-Table. The z- table use to determine the area under the standard normal curve for any value between the mean (zero) and any z-score.

(a) The value of [tex]P(z>-1.13)=0.8708[/tex].

(b) The value of  [tex]P(Z < 0.18) = 0.5714[/tex].

(c) The value of [tex]P(Z > 8) = 0.0000[/tex].

(d) The value of [tex]P(| Z | < 0.5) =0.3830[/tex].

Given:

The given condition is [tex]Z\sim N(\mu= 0,\sigma = 1).[/tex]

(a)

Find the value for [tex]P(Z > -1.13)[/tex].

Here Z is less than 1 that means Z is negative. So it will lies it lies on left hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area = 0.3708[/tex].

Now,

[tex]P(Z > -1.13)=0.5 + 0.3708 = 0.8708[/tex]

Thus, the value of [tex]P(z>-1.13)=0.8708[/tex].

(b)

Find the value for [tex]P(Z < 0.18)[/tex].

Here Z is positive. So it will lies it lies on right hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area = 0.0714[/tex].

Now,

[tex]P(Z <0.18)=0.5 + 0.0714 = 0.5714[/tex]

Thus, the value of  [tex]P(Z < 0.18) = 0.5714[/tex].

(c)

Find the value for [tex]P(Z >8)[/tex].

Here Z is positive. So it will lies it lies on right hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area \approx 0.5[/tex].

Now,

[tex]P(Z >8)\approx0.5 - 0.5 = 0.0000[/tex]

Thus, the value of [tex]P(Z > 8) = 0.0000[/tex].

(d)

Find the value for [tex]P(|Z| <0.05)[/tex].

Here Z is mod of Z, it may be positive or negative. Consider the negative value of Z.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area =0.1915[/tex].

Consider the positive  value of Z.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area =0.1915[/tex].

Now,

[tex]P(|Z| <0.5)=2\times 0.1915 = 0.3830[/tex]

Thus, the value of [tex]P(| Z | < 0.5) =0.3830[/tex].

Learn more about z-table here:

https://brainly.com/question/16051105

Answer:

-3/2

Step-by-step explanation:

Hey there!

Well to find the slope of a line with 2 points we use the following formula,

y2 - y1 / x2 - x1

5 - 2 = 3

-6 - -4 = -2

Slope = -3/2

Hope this helps :)

Answer:

[tex]Slope = -\frac{3}{2}[/tex]

Step-by-step explanation:

[tex](-4, 2) \:(-6,5).\\\\m =\frac{y_2-y_1}{x_2-x_1} \\\\x_1 = -4\\y_1 =2\\x_2 = -6\\y_2 =5\\\\m = \frac{5 -2}{-6-(-4)}\\ m = \frac{3}{-6+4}\\ m = \frac{3}{-2}\\ \\Slope = -\frac{3}{2}[/tex]

Answer: A) 15

Step-by-step explanation:

Because of Pythagorean Theorem, 9^2+12^2=BC^2.  Thus, 81+144=BC^2.  Thus, 225=BC^2.  Thus, 15=BC.

Hope it helps, and ask if you want further clarification <3

Answer:

c ≤ -9

Step-by-step explanation:

c / -3 ≥ 3

c ≤ -9

Remember, we flip the sign of the inequality by multiplying / dividing by a negative number.

Answer:

c ≤ -9

Step-by-step explanation:

c / -3 ≥ 3

c ≤ -9

Answer:

[tex]\boxed{Option \ B}[/tex]

Step-by-step explanation:

In the triangle,

Hypotenuse = 13

Opposite = Perpendicular = 5

Adjacent = Base = 12

Now,

Cos B = [tex]\frac{Adjacent}{Hypotenuse}[/tex]

Cos B = 12/13

If the triangle is just like in the attached file!

Answer:

B) 12/13

Step-by-step explanation:

Answer:

a) 30%

b) 45%

Step-by-step explanation:

a) Laura rolls it '4' 12/40 times, you need to convert that to a percent, so 12/40=6/20= 30% or 30/100

b) Basically the same thing: 18/40 = 45% or 45/100

Hope this helped XD

Answer:

[tex]7\frac{3}{20}[/tex]

Step-by-step explanation:

Hey there!

Well to add this we need to pu it in improper form.

7/5 + 23/4

Now we need to find the LCM.

5 - 5, 10, 15, 20, 25, 30

4 - 4, 8, 12, 16, 20, 24, 28

So the LCD is 20.

Now we need to change the 5 and 4 to 20.

5*4 = 20

7*4 = 28

28/20

4*5=20

23*5=115

115/20

Now we can add 28 and 115,

= 143/20

Simplified

7 3/20

Hope this helps :)

Answer:

Step-by-step explanation:

[tex] \mathrm{1 \frac{2}{5} + 5 \frac{3}{4} }[/tex]

Add the whole numbers and fractional parts of the mixed numbers separately

[tex] \mathrm{ = (1 + 5) + ( \frac{2}{5} + \frac{3}{4} })[/tex]

Add the numbers

[tex] \mathrm{=6 + ( \frac{2}{5} + \frac{3}{4} )}[/tex]

Add the fractions

[tex] \mathrm{=6 + (\frac{2 \times 4 + 3 - 5}{20} )}[/tex]

[tex] \mathrm{=6 + \frac{23}{20} }[/tex]

Convert the improper fractions into a mixed number

[tex] \mathrm{=6 + 1 \frac{3}{20} }[/tex]

Write the mixed number as a sum of the whole number and the fractional part

[tex] \mathrm {= 6 + 1 + \frac{3}{20} }[/tex]

Add the numbers

[tex] \mathrm{ = 7 + \frac{3}{20} }[/tex]

Write the sum of the whole number and the fraction as a mixed number

[tex] \mathrm{ = 7 \frac{3}{20} }[/tex]

Hope I helped

Best regards!

Answer:

.

Step-by-step explanation:

Answer:

[tex]\boxed{x^3+6x^2+9x}[/tex]

Step-by-step explanation:

[tex]x(x+3)(x+3)[/tex]

Resolving the first parenthesis

[tex](x^2+3x) (x+3)[/tex]

Using FOIL

[tex]x^3+3x^2+3x^2+9x[/tex]

Adding like terms

[tex]x^3+6x^2+9x[/tex]

[tex]\text{If } \: a\cdot b \cdot c = 0 \text{ then } a=0 \text{ or } b =0 \text{ or } c=0 \text{ or all of them are equal to zero.}[/tex]

[tex]x(x+3)(x+3) =0[/tex]

[tex]\boxed{x_1 =0}[/tex]

[tex]x_2+3 =0[/tex]

[tex]\boxed{x_2 = -3}[/tex]

[tex]x_3+3 =0[/tex]

[tex]\boxed{x_3 = -3}[/tex]

Answer: try using sine for this equasion

Step-by-step explanation:

Answer:

[tex]\boxed{3}[/tex]

Step-by-step explanation:

We can use ratios to solve since the sides are proportional.

[tex]\frac{18}{x} =\frac{48}{8}[/tex]

Cross multiply.

[tex]48x=18 \times 8[/tex]

Divide both sides by 48.

[tex]\frac{48x}{48} = \frac{18 \times 8}{48}[/tex]

[tex]x=3[/tex]

The value of x in the given triangle is 3.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Given are two similar triangles,

Therefore, they have the same ratio of corresponding sides

18/48 = x/8

x = 3

Hence, The value of x in the given triangle is 3.

For more references on similar triangles, click;

https://brainly.com/question/25882965

#SPJ2

Answer: Regression line equation:  [tex]\hat{y}=-1.008x+39.1704[/tex]

Step-by-step explanation:

Equation of least-squares regression line for predicting y :

[tex]\hat{y}=b_1x+b_o[/tex]

, where [tex]\text{Slope} (b_1)=r\dfrac{s_y}{s_x}[/tex] ,  [tex]\text{intercept}(b_0)=\bar{y}-b_1\bar{x}[/tex]

Given: [tex]\bar{x}=8.8,\ s_x=1.5,\ s_y=1.8,\ \bar{y}=30.3,\ r=-0.84[/tex]

Then,

[tex]b_1=(-0.84)\dfrac{ 1.8}{ 1.5}\\\\\Rightarrow\ b_1=-1.008[/tex]

Now,

[tex]b_0=30.3-(-1.008)(8.8)=30.3+8.8704\\\\\Rightarrow\ b_0=39.1704[/tex]

Then, Regression line equation:  [tex]\hat{y}=-1.008x+39.1704[/tex]

Answer:

(2x - y)³ = 8x³ - 12x²y + 6xy² - y³

Step-by-step explanation:

Pascal's Theorem uses a set of already known and easily obtainable numbers in the expansion of expressions. The numbers serve as the coefficients of the terms in the expanded expression.

For the expansion of

(a + b)ⁿ

As long as n is positive real integer, we can obtain the coefficients of the terms of the expansion using the Pascal's triangle.

The coefficient of terms are obtained starting from 1 for n = 0.

- For the next coefficients of terms are 1, 1 for n = 1.

- For n = 2, it is 1, 2, 1

- For n = 3, it is 1, 3, 3, 1

The next terms are obtained from the previous one by writing 1 and summing the terms one by one and ending with 1.

So, for n = 4, we have 1, 1+3, 3+3, 3+1, 1 = 1, 4, 6, 4, 1.

The Pascal's triangle is

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 1

1 9 36 84 126 126 84 36 9 1

The terms can also be obtained from using the binomial theorem and writing the terms from ⁿC₀ all through to ⁿCₙ

So, for n = 3, the coefficients are 1, 3, 3, 1

Then the terms are written such that the sum of the powers of the terms is 3 with one of the terms having the powers reducing from n all through to 0, and the other having its powers go from 0 all through to n

So,

(2x - y)³ = [(1)(2x)³(-y)⁰] + [(3)(2x)²(-y)¹] + [(3)(2x)¹(-y)²] + [(1)(2x)⁰(-y)³]

= (1×8x³×1) + (3×4x²×-y) + (3×2x×y²) + (1×1×-y³)

= 8x³ - 12x²y + 6xy² - y³

Hope this Helps!!!

Answer:

Yes, the confidence interval contradict this statement.

Step-by-step explanation:

The complete question is attached below.

The data provided is:

[tex]n_{1}=318\\n_{2}=297\\\bar x_{1}=25\\\bar x_{2}=24.1\\s_{1}=3.6\\s_{2}=3.8[/tex]

Since the population standard deviations are not provided, we will use the t-confidence interval,

[tex]CI=(\bar x_{1}-\bar x_{2})\pm t_{\alpha/2, (n_{1}+n_{2}-2)}\cdot s_{p}\cdot\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}[/tex]

Compute the pooled standard deviation as follows:

[tex]s_{p}=\sqrt{\frac{(n_{1}-1)s_{1}^{2}+(n_{2}-1)s_{2}^{2}}{n_{1}+n_{2}-2}}=\sqrt{\frac{(318-1)(3.6)^{2}+(297-1)(3.8)^{2}}{318+297-2}}=2.9723[/tex]

The critical value is:

[tex]t_{\alpha/2, (n_{1}+n_{2}-2)}=t_{0.05/2, (318+297-2)}=t_{0.025, 613}=1.962[/tex]

*Use a t-table.

The 95% confidence interval is:

[tex]CI=(\bar x_{1}-\bar x_{2})\pm t_{\alpha/2, (n_{1}+n_{2}-2)}\cdot s_{p}\cdot\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}[/tex]

     [tex]=(25-24.1)\pm 1.962\times 2.9723\times \sqrt{\frac{1}{318}+\frac{1}{297}}\\\\=0.90\pm 0.471\\\\=(0.429, 1.371)\\\\\approx (0.43, 1.37)[/tex]

The 95% confidence interval for the difference between the mean weights is (0.43, 1.37).

To test the magazine's claim the hypothesis can be defined as follows:

H₀: There is no difference between the mean weight of 1-year old boys and girls, i.e. [tex]\mu_{1}-\mu_{2}=0[/tex].

Hₐ: There is a significant difference between the mean weight of 1-year old boys and girls, i.e. [tex]\mu_{1}-\mu_{2}\neq 0[/tex].

Decision rule:

If the confidence interval does not consists of the null value, i.e. 0, the null hypothesis will be rejected.

The 95% confidence interval for the difference between the mean weights does not consists the value 0.

Thus, the null hypothesis will be rejected.

Conclusion:

There is a significant difference between the mean weight of 1-year old boys and 1-year old girls.