Claire keeps track of the miles per gallon her car gets per week. She has accumulated the following data: (1, 22.42), (2, 22.84), (3, 23.26), (4, 23.68) What is the common difference or ratio

An undecidable problem is one that should have a "yes" or "no" answer but has no algorithm that can correctly answer on all inputs.

According to the theories of computational complexity and computability, an undecidable problem is one for which it has been demonstrated that it is impossible to create an algorithm that always yields the right yes-or-no response. As an illustration, it can be shown that there is no algorithm that can accurately predict whether arbitrary programmes will eventually halt when run.

Any question that is simply yes or no on an infinite list of inputs is a decision problem. It is customary to define the decision problem as the set of inputs for which the problem returns yes because of this. Natural numbers as well as values of other kinds, such as strings in a formal language, can be used as these inputs.

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The absolute value of the test t-score is less than the absolute value of the critical t-score, there is not enough evidence to say that the population mean has changed.

population mean assumed to be 2925

sample mean = 2515

standard deviation of sample = 585.

sample size = 15

t-score is indicated because the standard deviation is taken from the sample rather than from the population.

t-score = (x - m) / s

x is the raw score

m is the raw mean of the population

s = standard deviation of sample/sqrt (sample size) = 585/sqrt(15) = 151.6217 rounded to 4 decimal places.

degrees of freedom = 15 minus 1 = 14.

t-score = (2515 - 2925)/151.6217 = -2.7123 rounded to 4 decimal places.

you need to know the confidence level.

at a 95% confidence level, the two-tailed critical t-score with 14 degrees of freedom = plus or minus 1.7613 rounded to 4 decimal places.

since the absolute value of the test t-score is less than the absolute value of the critical t-score, there is not enough evidence to say that the population mean has changed.

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Mean distance for group A = 6.01 miles and for group B = 2.17 miles.

In statistics, the mean is the average of all data values given in a data set.

Mean is calculated by adding all the data value and then divided the sum by the total amount of data.

distance in miles for Group A       distance in miles for group B

         11.5                                                  2

          8                                                  

                                                                2.5

         9.2                                                3.23

         6.8                                                 1.3

          4.5                                                1.8

          4.8                                                2.4

         2.5                                                 3

         0.76                                               1.5

                                                                1.8

now mean value for group A = sum of data value/ number of data value

  mean distance = (11.5 + 8 +9.2 +6.8 +4.5+ 4.8+2.5+0.76) / 8

  mean distance for group A = 6.01 miles

mean distance for group B = (2+2.5+3.23+1.3+1.8+2.4+3+1.5+1.8)/ 9

 mean distance = 2.17 miles

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In order to get the value of n, which is what we are trying to find, it is important to know how to isolate the variable.

When something is added to n, you subtract to isolate n. Going with this logic, you would multiply by a number if you wanted to isolate n with a fraction.

[tex]\frac{n}{5}+4=-4[/tex]

The first step would be to get rid of the 4 on the left side so we can work on the variable. We can do this by subtracting both sides by 4, so the left side cancels out to 0.

[tex]\frac{n}{5}+4-4=-4-4[/tex]

[tex]\frac{n}{5} =-8[/tex]

Next, we can multiply both sides by 5, so we can isolate the variable, because it is being divided by 5.

[tex]\frac{n}{5} *5=-8*5[/tex]

n=-40

The probability of the event that the mean amount of water in the 16 bottles is within 5 mL of the population mean is approximately 0.9544, which is closest to 0.95.

The correct answer is: D. P(500 <<510) 0.95.

Here, we have to find the probability that the mean amount of water in the 16 bottles is within 5 mL of the population mean (505 mL), we need to calculate the probability P(500 <x < 510), where x is the sample mean.

Given that the sample size (n) is 16 and the population standard deviation (σ) is 10 mL, we can use the Central Limit Theorem to approximate the sampling distribution of the sample mean.

The Central Limit Theorem states that for a sufficiently large sample size (n ≥ 30), the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

The mean of the sampling distribution of the sample mean is equal to the population mean (μ) and the standard deviation of the sampling distribution (standard error) is given by σ/√n, where σ is the population standard deviation and n is the sample size.

In this case:

μ = 505 mL (population mean)

σ = 10 mL (population standard deviation)

n = 16 (sample size)

The standard error (SE) of the sample mean is:

SE = σ/√n = 10/√16 = 10/4 = 2.5 mL

Now, we need to find the z-scores for 500 mL and 510 mL:

z₁ = (500 - μ) / SE = (500 - 505) / 2.5 = -2

z₂ = (510 - μ) / SE = (510 - 505) / 2.5 = 2

Using the z-table or a statistical calculator, we can find the probabilities corresponding to these z-scores:

P(z < -2) ≈ 0.0228

P(z < 2) ≈ 0.9772

Now, to find the probability that the sample mean is within 5 mL of the population mean (P(500 <x < 510)), we subtract the probability corresponding to the lower z-score from the probability corresponding to the higher z-score:

P(500 < x < 510) ≈ P(z < 2) - P(z < -2) ≈ 0.9772 - 0.0228 ≈ 0.9544

So, the probability of the event that the mean amount of water in the 16 bottles is within 5 mL of the population mean is approximately 0.9544, which is closest to 0.95.

The correct answer is: D. P(500 <<510) 0.95

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Answer:

To find the number of three-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6, with repetition allowed, we can use the formula for permutations:

Step-by-step explanation:

Number of permutations = (number of choices for the first digit) x (number of choices for the second digit) x (number of choices for the third digit)

In this case, we have 6 choices for each digit, since we are allowed to repeat the digits. Using the formula, we get:

Number of permutations = 6 x 6 x 6 = 216

Therefore, there are a total of 216 three-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6, with repetition allowed.

However, not all of these will be even. For a number to be even, the last digit must be even, so the last digit can only be 2, 4, or 6. This means that there are 3 choices for the last digit.

Therefore, the total number of even 3-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6 is 366=108.

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Based on this information, Gregory can make a valid conclusion.

Sampling methods are methods used to create a sample in for a survey. There are probability sampling methods as well as non probability sampling methods.

Given sampling method done by two students, Mike and Gregory, to choose a sample of students to survey the students interested in summer camp.

Names of students are listed in an alphabetical order.

Mike chooses the name of every student in 7th grade on the list and Gregory chooses the name of every 3rd student on the list.

The sampling of Mike will lead to sampling bias. Here the conclusion which can be made about the total population is weaker because only the students of particular class is attending. Conclusions may be more limited.

Whereas in the case of sampling of Gregory, he uses one of the probability sampling method called systematic sampling method. The sampling using probability sampling method is more convenient as it has less sampling bias as well as research bias.

Hence Gregory can make a valid conclusion in this case.

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The sample size needed for a margin of error of 1%, for a confidence level of 90%, is of:

6,766.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The margin of error of the interval is defined as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.90}{2} = 0.95[/tex], so the critical value is z = 1.645.

We have no prior estimate, hence the proportion is given as follows:

[tex]\pi = 0.5[/tex]

For a margin of error of M = 0.01, the needed sample size n is obtained as follows:

[tex]0.01 = 1.645\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.01\sqrt{n} = 1.645 \times 0.5[/tex]

[tex]\sqrt{n} = \frac{1.645 \times 0.5}{0.01}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.645 \times 0.5}{0.01}\right)^2[/tex]

n = 6,766.

(rounding up, as for a sample size of 6,765 the margin of error would be slightly above 0.01).

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Answer: D

Step-by-step explanation:

In this problem, we are asked to find the domain of the function. Domain is finding the interval of the function of the x value.

Since we are finding domain, we can eliminate A and B because those are looking at y interval, or range.

This leaves us with C and D. They are almost the same except for the ≤ in C and < in D. The difference between ≤ and < is the fact that ≤ includes and touches the point, and < doesn't.

The function has open circles at x=-3 and x=3. That means they don't touch and include x=-3 and x=3. The function only get's really close to those points, but not include them. This tells us that D is the answer.

The domain of the function is {x | −3 < x < 3}. Thus, Option D holds the truth.

The domain of a function refers to the interval of the x values of the function.

In this case, we are asked to find the domain of a linear function that is shown on a graph. The graph starts at an open circle at negative 3, negative 5 and ends at an open circle at 3, 7.

To find the domain, we need to look at the x interval of the function. Options A and B refer to the y interval or range and can be eliminated.

The remaining options, C and D, are similar, except for the fact that C includes and touches the point with "≤", while D doesn't with "<". The open circles at x=-3 and x=3 indicate that the function only gets close to these points, but does not include or touch them.

Thus, the correct answer is option D, {x | −3 < x < 3}.

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Answer:

u = 8

Step-by-step explanation:

calculate the slope of the line passing through the 2 give points using the slope formula, then equate to the given slope.

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 5, 5 ) and (x₂, y₂ ) = (5, u )

m = [tex]\frac{u-5}{5-(-5)}[/tex] = [tex]\frac{u-5}{5+5}[/tex] = [tex]\frac{u-5}{10}[/tex] , then equating the 2 expressions gives

[tex]\frac{u-5}{10}[/tex] = [tex]\frac{3}{10}[/tex] ( cross- multiply )

10(u - 5) = 30 ( divide both sides by 10 )

u - 5 = 3 ( add 5 to both sides )

u = 8

Step-by-step explanation:

(u - 5)/(5 + 5)= 3/10

(u - 5)/10= 3/10

10u - 50 = 30

10u = 80

u = 8

The solution of the equation is x = 6, y = 0.

1. Subtract the two equations:

   x3y6 - 2x3y12 = 0

2. Simplify both sides of the equation:

   x3y - 2x3y = 0

3. Simplify further calculations:

   x3(y - 2y) = 0

4. Factorize the expression:

   x(y - 2y) = 0

5. Solve for x:

   x = 0

6. Substitute x = 0 into either equation:

   3y = 6

7. Solve for y:

   y = 2

8. Substitute y = 2 into either equation given above:

   x = 6

The solution of the equation is x = 6, y = 2.

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Answer:

1/4 of 60= 15

15+60=75

75 is 125% of 60

Step-by-step explanation:

To calculate log 10 on a calculator, you will typically use the "log" button. Depending on the type of calculator, you may need to enter the number 10 first, then hit the "log" button.

For example, if using a standard scientific calculator, you would enter 10, then hit the "log" button. On some calculators, you may need to hit the "10x" button first before hitting the "log" button.  On some graphing calculators, you may need to use the "log base" button. When using this button, you would enter 10 as the base and the number you are trying to calculate the log of.

In some cases, you may need to use the "ln" (natural log) button instead of the "log" button. In this case, you would need to use the conversion formula of "ln x = 2.303 log 10 x" to get the desired number.  Finally, some calculators may have an "antilog" button. This button will calculate the inverse of the logarithm or the power of 10 of a given number. To use this button, you would enter the number, then press the antilog button.

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The number of hours that the team trians per week is 17 hours.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since the the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. The number of hours will be:

( 1 1/4 + 1/2 + 2 1/2) × 4

= 4.25 × 4

= 17 hours.

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The degree of the polynomial x4 x3 5x 3 is 4, since it is the highest degree of the polynomial.

A polynomial is an expression that consists of variables, coefficients, and operators such as addition, subtraction, multiplication, and division. It is used to represent a mathematical relationship between variables. The degree of a polynomial is the highest power that appears in the expression, and it indicates the number of terms that make up the polynomial. Polynomials are usually written in descending order of powers, and the highest power is the leading term.

The highest degree of any polynomial is considered its degree. It is also referred to as the degree of the polynomial's leading term, since it is the highest power of x. In this case, the leading term is x4.

The degree of a polynomial can be used to classify the type of polynomial it is. For example, if the degree of a polynomial is 2, it is a quadratic polynomial. Similarly, if the degree of a polynomial is 3, it is a cubic polynomial.

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Answer:

The hundreds place

Step-by-step explanation:

143, first digit is , 1 is in the hundreds place

Based on the 2:5 quantity of concentrate and water, the amount of water required for 90 mililitres will be 225 mililitres of water.

Firstly we will be creating the ratio for the mentioned information. It will be as follows-

Amount of concentrate/Amount of water

The proportion will be -

2/5 = 90/Concentration of water

Concentration of water = 90×5/2

Now perform multiplication in numerator on Right Hand Side of the equation

Concentration of water = 450/2

Then work out the division on Right Hand Side of the equation

Concentration of water = 225 mililitres

Thus, the required amount of water is 225 mililitres.

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The value of x in the triangle WXY is 19 degrees

An equation shows how two or more numbers and variables are related to each other.

From the question, we have the following parameters that can be used in our computation:

The triangle XYZ and the line YZ such that lie YZ and XW are parallel lines

Using the above as a guide, we have the following:

∠ZYW = ∠XWY (alternate angles are equal)

∠XWY = 2x (Given)

So, we have

∠XWY + ∠XYW + ∠YXW = 180° (the sum of angles in a triangle)

Substitute the known values in the above equation, so, we have the following representation

2x + (3x - 5) + 90 = 180

Open the brackets and solve

5x - 5 = 90

Evaluate the like terms

5x = 95

Divide both sides by 5

x = 19°

Hence, the value of x is 19°

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One cannot add themselves directly to Wikipedia as this can cause harm to the platform and community in a later run. As one can start adding content and details on the page based on their personal opinions.

Therefore we can say that  the answer is that we cannot edit or create our own Wikipedia page, because that would be a conflict of interest ,more on this later.

But the thing which one can do is to add themselves in the line ,to list themselves on Wikipedia’s repository of articles which are out there looking for creators who can help maintain the site.

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Answer:

The area of the dog pen is 522 [tex]ft^2[/tex].    (feet squared)

The perimeter of the dog pen is 94 feet

Step-by-step explanation:

Area

Here is the formula for the area of a rectangle.

[tex]A=lw[/tex]

We are given

[tex]l=29\\w=18[/tex]

Lets evaluate [tex]A[/tex].

[tex]A=29*18\\A=522[/tex]

Perimeter

Here is the formula for the perimeter of a rectangle.

[tex]P=2w+2l[/tex]

We are given

[tex]l=29\\w=18[/tex]

Lets evaluate [tex]P[/tex].

[tex]P=2l+2w\\P=(2*29)+(2*18)\\P=58+(2*18)\\P=58+36\\P=94[/tex]

Answer:

b

Step-by-step explanation:

i think b because it makes more sense than a or c

Answer:

12² = 144

12 to the power of 2 us equal to 144

To determine whether the point [tex](1,2)[/tex] is a solution of inequality  [tex]3x - 2y - 6 > 0[/tex],  we substitute the point in the inequality and if the result is True, then it will be the solution .

What is an Inequality ?

The Inequality is defined as a relationship between two expressions or values that are not equal to each other .

The inequality in the question is given as : [tex]3x - 2y - 6 > 0[/tex] ;

the point is ⇒ [tex](1,2)[/tex] ,

to check the solution , we substitute the values in the inequality as [tex]x=1[/tex]and [tex]y=2[/tex] ;

we get , [tex]3(1) -2(2) - 6 > 0[/tex]

= [tex]3-4-6 > 0[/tex]

= [tex]3-10 > 0[/tex]

= [tex]-7 > 0[/tex],

But we know that , [tex]-7 < 0[/tex] , So , the given point is not the solution of the given inequality .

The given question is incomplete , the complete question is

How do you determine if the given point (1,2)  is a solution of each linear inequality 3x - 2y - 6 > 0  ?

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Answer:

There are 47 dimes and 2 pennies.

Step-by-step explanation:

10¢ = 1 dime

$4.70 = 470 ¢

470 dimes = 47 dimes

and 2 pennies

Answer:

$899.54

Step-by-step explanation:

To find the cost of sod for a trapezoid shaped yard, we need to first find the area of the trapezoid. The formula for the area of a trapezoid is:

Area = (1/2) * h * (b1 + b2)

where h is the height of the trapezoid and b1 and b2 are the lengths of the bases.

Substituting the given values, we get:

Area = (1/2) * 46 ft * (78 ft + 111 ft)

= (1/2) * 46 ft * 189 ft

= 4274 ft^2

To find the cost of sod for this area, we need to multiply the area by the cost per square foot of sod. The cost will be:

Cost = 4274 ft^2 * $0.21/ft^2

= $899.54

So the cost of sod for this yard will be $899.54.

Answer:

-2x + 10

Step-by-step explanation:

Apply the distributive law:  a(b - c) = ab - ac

-2(x - 5 ) = -2x - ( -2) x 5

= - 2x - ( - 2 ) x 5

- ( -2 ) x 5 = 10

= -2x + 10

Therefore, the multiple of the given equations is 10x^2yz + 6xyz^2, 5x^3y^2 + 14x^3y^3, and -10x^5 + 15x^4 - 30x^3 + 40x^2.

The process of multiplying two or more polynomials together is known as polynomial multiplication. Applying the distributive property to the multiplication of polynomials allows us to conduct polynomial multiplication.

Multiplication in mathematics is essentially just adding a number repeatedly in relation to another number. For instance, if we multiply 2 by 3, then implies that 3 gets multiplied by itself twice, meaning 3 + 3 = 6. Children can multiply numbers easily with the help of this method.

1. (5xy+3yz) * 2xz = 10x^2yz + 6xyz^2

2. (6/7x2y) * (35/6xy + 14/3 xy2) = 5x^3y^2 + 14x^3y^3

3. (2x3-3x2+6x-8) * (-5x2) = -10x^5 + 15x^4 - 30x^3 + 40x^2

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Answer:

[tex] \sf \: 7.31[/tex]

Step-by-step explanation:

Now we have to,

→ round a number to 2 decimal places.

The number is,

→ 7.3084

Let's solve the problem,

→ 7.3084

→ ≈ 7.308

→ [tex] \boxed{ \sf ≈ 7.31} [/tex]

→ ≈ 7.3

Hence, the answer is 7.31.

Answer:37.68

Step-by-step explanation:

given:

diameter of cylinder =4in.

radius of cylinder=2in.

height of cylinder =3in.

Volume of cylinder=πr^2h

. = 3.14×2×2×3

. = 37.68 in Cube

Answer:

113.1

Step-by-step explanation:

If π= 3.14 And The Equation For This Type Of Problem Is V=πr2h then all you do is do 3.14 times 9 times 4

Where Your Multiplying 3 To Square Of 2 To Get 9, So Take that 3.14 Multiply It By 9 And Then 14, Thus the answer is 113.1

Hope This Helps

Answer:

f(-7) = -33

Step-by-step explanation:

f(x) = − x² - 4x – 12

f(-7) = ?

We put -7 in for x and solve

f(-7) = -(-7)^2 -4(-7) - 12

f(-7) = -(49) + 28 - 12

f(-7) = -49 + 28 - 12

f(-7) = -33