Select the reason that best supports statement 5 in the given proof.

The solutions to the questions are given below

a)

sample(n) word length sample mean

1                    5,4,4,2    3.75

2                    3,2,3,6     3.5

3                         5,6,3,3    4.25

b)R =0.75

c)

The table below shows sample means in the table.

sample(n) word length sample mean

1                    5,4,4,2    3.75

2                    3,2,3,6     3.5

3                         5,6,3,3    4.25

b)

Generally, the equation for is  mathematically given as

variation in the sample means

R =maximum -minimum

R=4.25-3.5

R =0.75

c)

In conclusion, In most cases, the mean of many samples will provide a more accurate estimate than the mean of a single sample.

They may have a higher level of confidence in their estimate if the range of the sample means is closer to 0 than it is now.

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There is a maximum value of 6 located at (x, y) = (1, 6).

The function given to us is f(x, y) = xy.

The constraint given to us is 6x + y = 12.

Rearranging the constraint, we get:

6x + y = 12,

or, y = 12 - 6x.

Substituting this in the function, we get:

f(x, y) = xy,

or, f(x) = x(12 - 6x) = 12x - 6x².

To find the extremum, we differentiate this, with respect to x, and equate that to 0.

f'(x) = 12 - 12x ... (i)

Equating to 0, we get:

12 - 12x = 0,

or, 12x = 12,

or, x = 1.

Differentiating (i), with respect to x again, we get:

f''(x) = -12, which is less than 0, showing f(x) is maximum at x = 1.

The value of y, when x = 1 is,

y = 12 - 6x,

or, y = 12 - 6*1 = 6.

The value of f(x, y) when (x, y) = (1, 6) is,

f(x, y) = xy,

or, f(x, y) = 1*6 = 6.

Thus, there is a maximum value of 6 located at (x, y) = (1, 6).

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The provided question is incomplete. The complete question is:

"Find the extremum of f(x, y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x, y)=xy; 6x+y=12.

If the ratio of model train to real train is 1:3 and the real train is 12 feet then the model train is 3 feet long.

Given that the model train has a scale of 1:3 and the real train is 12 feet tall.

We are required to find the height of the model train.

Ratio shows how many times one number contains another number. A ratio is the relationship in quantity  between two things. It expresses quantity of one thing in terms of another.

Ratio of model train to real train is 1 inches :3 inches.

Height of model train=12*1/4

=3 inches

Hence if the ratio of model train to real train is 1:3 and the real train is 12 feet then the model train is 3 feet long.

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Answer:

B

Step-by-step explanation:

B Rounded to nearest ten thousand

The attendance that aligns with rounding to 120,000 is B) 116,390.

To determine the possible attendance at the amusement park if it was rounded to the nearest ten thousand, we need to consider the rounding process.

When rounding to the nearest ten thousand, we look at the digit in the ten thousand place. If this digit is 5 or greater, we round up to the next ten thousand. If it is less than 5, we round down to the previous ten thousand.

In this case, the attendance was rounded to 120,000. To round to the nearest ten thousand, we look at the digit in the ten thousand place, which is 2. Since 2 is less than 5, we round down.

Therefore, the attendance at the amusement park could have been rounded to 120,000 people if it was rounded to the nearest ten thousand.

Among the given options, the attendance that aligns with rounding to 120,000 is B) 116,390.

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Yes, the correlation coefficient is statistically significance

The precise metric used in a correlation analysis to quantify the strength of the linear relationship between two variables is the correlation coefficient. In a correlation report, the r stands for the coefficient.

Given,

Sample size, n = 4

Where ρ is the population correlation.

Then the number of degrees of freedom is, df = n-2 = 4-2 = 2

The corresponding critical correlation value re for a significance level of a 0.01, for a two-tailed test is た= 0.254

Here,

The null hypothesis, [tex]H_{0}[/tex] = ρ - 0 is rejected

Suppose lr> re 0.254

Because on the sample correlation provided, we know that lrl = 0.835>=0.254.

Here, it is clear that the null hypothesis is rejected.

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Answer:

..........................................

Step-by-step explanation:

let's name the variables for the age of the people as the people themselves :

orlando = omar + 12

carl = 3×orlando

carl + orlando + omar = 68

using the first equation in the second equation, and then that result and the first equation in the third equation :

carl = 3×(omar + 12)

3×(omar + 12) + (omar + 12) + omar = 68

3×omar + 36 + omar + 12 + omar = 68

5×omar + 48 = 68

5×omar = 20

omar = 4

orlando = omar + 12 = 4 + 12 = 16

carl = 3×orlando = 3×16 = 48

the ratio omar : carl : orlando

4 : 48 : 16 = 1 : 12 : 4

the ratio of the area of the triangle to the area of the rectangle is 1: 2

The formula for calculating the area of a triangle is;

Area of triangle = 1/ 2 base × height

The formula for area of a rectangle is;

Area of a rectangle = length ×  width

From the information given, we have;

Now, let's substitute the values;

Area of a triangle = 1/ 2 × 11 × 4

Area of a triangle = 44/ 2 = 22m²

Area of a rectangle = 11 × 4

Area of a rectangle = 44m²

The ratio of the area of the triangle to the area of the rectangle is

= 22: 44

= 1 : 2

Thus, the ratio of the area of the triangle to the area of the rectangle is 1: 2

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Based on the calculations, the depth of tent is equal to 12 feet.

Based on the diagram (see attachment) and information provided, we can logically deduce the following parameters (points):

Next, we would determine the height of the right-angled triangle (ADC) by applying Pythagorean theorem:

AC² = AD² + DC²

AD² = AC² - DC²

AD² = 5² - 3²

AD² = 25 - 9

AD² = 16

AD = √16

AD = 4 feet.

Also, we would determine the area of the triangle (ABC):

Area = 1/2 × b × h

Where:

Substituting the given parameters into the formula, we have;

Area = 1/2 × 6 × 4

Area = 12 feet².

Depth of tent = 3 × height of ADC

Depth of tent = 3 × 4

Depth of tent = 12 feet.

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James is (B) 20 meters far from the finish line 9 seconds after the race has started.

To find the distance:

Therefore, James is (B) 20 meters far from the finish line 9 seconds after the race has started.

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The complete question is given below:

James covers a distance of 8 meters in the first second of a 100-meter race. Then, he sprints at a speed of 9 meters per second. How far is James from the finish line 9 seconds after the race has started?

a. 11

b. 20

c. 28

d. 80

[tex](x-1) ^ { 3 } -(x-2) ^ { 2 } =1[/tex]

[tex]x^{3}-3x^{2}+3x-1-\left(x-2\right)^{2}=1 [/tex]

[tex]x^{3}-3x^{2}+3x-1-\left(x^{2}-4x+4\right)=1 [/tex]

[tex]x^{3}-3x^{2}+3x-1-x^{2}+4x-4=1 [/tex]

[tex]x^{3}-4x^{2}+7x-1-4=1 [/tex]

[tex]x^{3}-4x^{2}+7x-5=1 [/tex]

[tex]x^{3}-4x^{2}+7x-5-1=0 [/tex]

[tex]x^{3}-4x^{2}+7x-6=0 [/tex]

[tex]±6,±3,±2,±1 [/tex]

Answer:

Option D is correct.

No solution

Step-by-step explanation:

2(x+7)=8

Apply 2 into bracket:

2x+14=8

2x=8-14

2x=-6

Divide both sides by 2:

x=-3

hence here is no option for x=-3, so answer is no solution.

Anais bought 2 1/2 yards of ribbon. She had 2 feet 8 inches of ribbon left after trimming some curtains. Anais uses 58 inches of ribbon to trim the curtains.

What is Unit Conversion?

Anais bought 2 1/2 yards of ribbon.

And she had 2 feet 8 inches left after trimming some curtains.

The first thing to do is to convert all units to inches;

From standard conversion rate.

1 yard  = 36 inches

As such  2 1/2 yards of ribbon in inches will be:

= 2 1/2 × 36 inches

= 5/2 × 36 inches

= 5 × 18 inches

= 90 inches of ribbon bought.

Similarly, since 1 foot  = 12 inches.

The amount of curtains left after trimming is:

= ( ( 2 × 12 ) + 8 )inches

= (24 + 8) inches

= 32 inches

If Anais bought 90 inches of ribbon and she had 32 inches of ribbon left after trimming some curtains.

It implies that the number of inches of ribbon that Anais used is:

= 90 inches - 32 inches

= 58 inches

Therefore, we can conclude that Anais used 58 inches of ribbon.

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The complete question is-

Anais bought 2 1/2 yards of ribbon. She had 2 feet 8 inches of ribbon left after trimming some curtains. How many inches of ribbon did Anais use to trim the curtains?

Anais used _____ inches of ribbon.

Answer:

204

Step-by-step explanation:

6*10=60

6*6=36

6*8=48

2((10*6)/2)=60

60+60+36+48=204

Answer:

30°

Step-by-step explanation:

To make sure it's complete

The number of decorative pillows did the realtor arrange on each twin bed and queen bed is 6 and 9 respectively.

let

x + y = 15

2x + y = 21

From equation (1)

x = 15 - y

2x + y = 21

2(15 - y) + y = 21

30 - 2y + y = 21

- 2y + y = 21 - 30

-y = -9

y = 9

Substitute y = 9 into

x + y = 15

x + 9 = 15

x = 15 - 9

x = 6

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[tex]58.41 < f(x) < 150[/tex] inequality represents the range of the exponential function that models this situation

The exponential decay function is as follows:

[tex]y = a(1-r)^t[/tex]

Here,

y = final value

a = initial value

r = decay rate

t = time taken

Given that:

a = 150 mg

r = 9% = 0.09

Then the next hour the amount of caffeine in the body will be:

[tex]y = a (1-r)^t\\y = 150 \times (1-0.09)^2[/tex] = 136.5

Similarly, after 10 hours the amount of caffeine in the body will be:

[tex]y = 150 \times (1- 0.09)^{10} = 58.41[/tex]

Then the inequality representing the range of the exponential function that models this situation is:

58.41 < f(x) < 150

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The area of the circle A and B is 86.54 inches and 124.62 mm

According to the statement

we have given that the radius of the circle A and b and we have to find the area of the given circle.

So, we know that the

The area enclosed by a circle of radius r is πr².

So, For area of the circle

For condition A :

diameter = 10.5 inches

then radius = 5.25

Area = πr²

Area = 3.14*27.56

Area = 86.54 inches

Now, For condition B :

radius = 6.3 mm

Area = πr²

Area = 3.14*39.69

Area = 124.62mm

So, The area of the circle A and B is 86.54 inches and 124.62 mm

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The polar coordinate of given cartesian coordinate (-6, -1) is

(6.08, 0.0523π)

In this question,

We have been given the cartesian coordinate (-6, -1)

We need to convert given cartesian coordinate to polar coordinates.

We know that the polar coordinates is of the form (r, θ)

where, r is the magnitude with r = [tex]\sqrt{x^{2}+ y^{2} }[/tex]

and θ is the angle associated with the coordinates which is given by           θ =  [tex]tan^{-1}(\frac{y}{x} )[/tex]

The magnitude of the given polar coordinate is,

⇒ r = [tex]\sqrt{x^{2}+ y^{2} }[/tex]

⇒  r = [tex]\sqrt{(-6)^{2}+ (-1)^{2} }[/tex]

⇒ r = [tex]\sqrt{36+ 1}[/tex]

⇒ r = [tex]\sqrt{37}[/tex]

⇒ r = 6.08

And the angle associated with the coordinate is,

⇒ θ =  [tex]tan^{-1}(\frac{-1}{-6} )[/tex]

⇒ θ =  [tex]tan^{-1}(0.167 )[/tex]

⇒ θ = 9.48°

⇒ θ = 0.0523π

So, the polar coordinate is (6.08, 0.0523π)

Therefore, the polar coordinate of given cartesian coordinate (-6, -1) is

(6.08, 0.0523π)

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The 99% confidence interval for the decrease in the defective rate after the reconfiguration is (-0.018, 0.086).

Let the random variable & parameters be;

x1 : Number of successes from group 1

x2 : Number of successes from group 2

p1: Proportion of successes in group 1

p2: Proportion of successes in group 2

n1 : number of trial in group 1

n2: number of trial in group 2

We are given;

x1 = 260

n1 =985

x2 = 194

n2 = 842

Thus;

p1 = 260/985

p1 =0.2640

p2 = 194/842

p2 = 0.2304

Constructing a (1 - α)100% confidence interval for proportion from the formula;

(p₁ - p₂) - z√[((p₁(1 - p₁)/n₁) + p₂(1 - p₂)/n₂)]

plugging in z = 2.576 and the values of p₁, p₂, n₁ and n₂, we have the confidence interval as;

(-0.0184631, 0.0855743)

Therefore the 99% confidence interval for the decrease in the defective rate after the reconfiguration is (-0.018, 0.086).

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Answer:

11%

Step-by-step explanation:

Lets find the new price with the monthly installment.

5+6.50(10)=70

Now the percentage of increase.

Find difference

70-63=7

Divide by original

7/63=0.11

Multiply by 100

0.11*100=11.1

Rounds to approximately 11%

Answer:

6x + 4y = 16

Step-by-step explanation:

2(3x + 2y = 8)

2(3x + 2y) = 2(8)

6x + 4y = 16

Answer:

6x+4y=16

Step-by-step explanation:

2 (3x+2y=8)

2×3x+2×2y=2×8

=6x+4y=16 ans.

The base side of the isosceles triangle in discuss as described in the task content is; 10cm.

According to the task content, the area of the isosceles triangle is 60 square cm.

Since, the length of its longest sides is 13 cm and since it follows from convention that the bisection of an isosceles triangle results in the formation of two right-triangles.

Consequently, it follows from Pythagoras triples that the height of each right triangle is 12 and its base is; 5.

Consequently, the base of the whole isosceles triangle is; 2 × 5 = 10cm.

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The maximum area of the enclosure is 562500 square feet

The function is give as:

V(x) = 1500x - x^2

Differentiate

V'(x) = 1500 -2x

Set to 0

2x = 1500

Divide by 2

x = 750

Substitute x = 750 in V(x) = 1500x - x^2

V(x) = 1500*750 - 750^2

Evaluate

V(x) = 562500

Hence, the maximum area of the enclosure is 562500 square feet

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The missing reason in step 8 is the substitution property.

It should be noted that according to substitution property, if x = y, then x can be substituted for y in any equation.

When a variable is equal to another variable, then the variables can be interchangeable.

In this case, the missing reason in step 8 is the substitution property.

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The computation shows that the maximum number of pants per employee that can be washed each week is 6.

The maximum number of pants per employee that can be washed each week will be:

7 + 4.5x + 12 <= 46

4.5x <= 27

x <= 6

The maximum number is 6.

The maximum number of chef coats per employee that can be washed each week will be:

= 6 + 8

= 14

The maximum total number of items per employee that can be washed in a week will be:

= 6 + 14 = 20

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Translate the triangle by [tex](^{-2}_{-4})[/tex] means translating 2 units left and 4 units down.

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.

Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.

Translate the triangle by [tex](^{-2}_{-4})[/tex] means translating 2 units left and 4 units down.

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After 16 days, the total homework questions that have been assigned would be 80 questions.

Ratio expresses the equivalent relationship between two numbers. It shows the frequency of the number of times that one value is contained within other value(s).

A ratio table can be described as table that shows equivalent values between two numbers.

The first step is to determine the ratio between the number of days and the total number of questions.

Ratio = money saved / money earned

8/10 =  total number of questions / number of days

55 / 11 = 5

Now, multiply the ratio gotten in the previous step by the number of days

Total number of homework questions = number of x ratio

5 x 16 = 80 questions

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