The spread of data set X is greater than the spread of data set Y, and the data sets are normally distributed. Which statement is true? The mean of data set X is greater than the mean of data set Y. The median of data set X is less than the median of data set Y. The standard deviation of data set X is greater than the standard deviation of data set Y. The range of data set X is less than the range of data set Y. The mode of data set X is greater than the mode of data set Y.

The quotient of any two rational numbers is always a rational number. This can be proved by expressing the division as multiplication by the reciprocal and demonstrating that the result is a rational number. Therefore, the property of being rational is preserved under division.

Let's define rational numbers first. A rational number is any number that can be expressed as the quotient of two integers, where the denominator is not zero. Mathematically, if a and b are integers and b ≠ 0, then r = a/b is a rational number.

Thus, we have proved that the quotient of any two rational numbers is a rational number.

The question is about calculus and requires finding the limit of a multivariable function as it approaches a particular point. Evaluating such limits can be very complex and typically requires application of theorems and techniques from multivariable calculus. In this specific case evaluation of limit goes beyond the scope of this platform.

The subject of this question is mathematics, specifically it is about

Calculus

and more specifically about finding limits of functions of multiple variables. In this case, the function given is f(x, y, z) =  (xy + 3yz2 + 4xz2) / (x2 + y2 + z4). To determine the limit of the function (if it exists) as (x, y, z) approaches (0, 0, 0), we would use substitution method. When we substitute x=0, y=0, and z=0 to the function, we get undefined format (0/0) which means we need to apply the L'Hopital's rule. But application of this rule to multivariable function involves evaluating multiple partial derivatives of function which is beyond the scope of this platform. Hence, a full evaluation of the limit of this particular function requires use of theorems and techniques from

multivariable calculus

.

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Answer: The area of the cover = 56 square inches.

Step-by-step explanation:

We know that the shape of a tablet is rectangle.

Thus to calculate the area of the protective cover we apply the formula to calculate area of rectangle.

The area of rectangle is given by :-

[tex]\text{Area}=\text{Length*width}\\\\\Rightarrow\text{Area}=8\times7\\\\\Rightarrow\text{Area}=56\text{ inches}^2[/tex]

Therefore, the area of the protective cover is 56 square inches.

multiply 19.7 x 4 for total gallons

19.7 * 4 = 78.8 total gallons

 multiply that by price:

78.8 * $3 = $236.40 total price

Mrs. Blanka spent $236.4 on gas last month by filling up her truck's 19.7-gallon tank 4 times at a price of $3 per gallon.

To calculate how much Mrs. Blanka spent on gas last month, we need to consider the amount of gas her truck holds, the number of times she filled up her tank, and the price per gallon of gas. Mrs. Blanka's truck holds 19.7 gallons of gas, and she used 4 full tanks of gas last month. Given the price of gas was $3 per gallon, the calculation would be as follows:

Therefore, Mrs. Blanka spent $236.4 on gas last month.

First let us calculate for his salary this year. We know that 3000 is only 8% of his salary, hence:

0.08 * salary = 3000

salary = 3000 / 0.08

salary = 37,500

Therefore his previous salary is:

previous salary = 37,500 + 2,000

previous salary = $39,500

Answer:

First let us calculate for his salary this year. We know that 3000 is only 8% of his salary, hence:

0.08 * salary = 3000

salary = 3000 / 0.08

salary = 37,500

Therefore his previous salary is:

previous salary = 37,500 + 2,000

previous salary = $39,500

Step-by-step explanation:

a) P(X >= 6) = 0.0160

b) P(X > 10) ≈ 6.88 x 10^-6

c) P(X = 0) ≈ 0.1339

d) P(X < 5) ≈ 0.9482

a. Probability of six or more pages with errors:

This is the sum of probabilities for 6, 7, 8, ..., 200 errors:

P(X >= 6) = 1 - [P(X < 6)] = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]

Using a calculator or statistical software, we can find these individual probabilities and sum them up. Alternatively, we can use binomial distribution tables or functions available in programming languages.

P(X >= 6) ≈ 0.0160

b. Probability of more than 10 pages with errors:

Similar to part (a), but calculating from 11 errors onwards:

P(X > 10) = 1 - [P(X=0) + P(X=1) + ... + P(X=10)]

P(X > 10) ≈ 6.88 x 10^-6 (very small probability)

c. Probability of none of the pages containing errors:

P(X = 0) = (0.99)^200 ≈ 0.1339

d. Probability of fewer than five pages containing errors:

P(X < 5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)

P(X < 5) ≈ 0.9482

Answer:

The value of the 7 in 507,264 is 10 times the value of the 7 in number 2

Step-by-step explanation:

Given Number : 507,264

To find : Number in which the value of the 7 in 507,264 is 10 times the value of the 7 .

Starting from the left ,

4 is in ones place

6 is in tens place

2 is in hundreds place

7 is in thousands place

0 is in ten thousands place

5 is in lakhs place

Here, 7 is in thousands place

7000 = 10 x 700

2 is in hundreds place

200 = 2 × 100

Therefore, the value of the 7 in 507,264 is 10 times the value of the 7 in  number 2 .

An equation is formed when two equal expressions. Max's total earnings for the given month are $4,325. The correct option is C.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that Max has a monthly salary of $1,100 and also earns a 7.5% commission on his sales. Therefore, the equation that can represent Max's monthly salary for any month is,

y = $1,100 + $(0.075x)

where y is the month's salary and x is the number of sales he made.

Given in the last month Max had $43,000 in sales last month. Therefore, Max's total salary for the given month is,

Max Salary = $1,100 + $(0.075x)

= $1,100 + $(0.075 × 43,000)

= $1,100 + $3,225

= $4,325

Hence, Max's total earnings for the given month are $4,325.

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To find (f+g)(x), add the functions f(x) and g(x), substituting x into both functions and then adding the results together. The result is (f+g)(x) = 4x + 16.

To find (f+g)(x), we need to add the two functions f(x) and g(x). f(x) = 3x + 7 and g(x) = x + 9. To determine (f+g)(x), we substitute x into both f(x) and g(x) and then add the results together.

So, (f+g)(x) = f(x) + g(x) = (3x + 7) + (x + 9) = 4x + 16.

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354,738 rounded to the nearest thousand is 355,000.

In Mathematics and Euclidean Geometry, a place value is a numerical value (number) which denotes a digit based on its position in a given number and it includes the following:

The number in the thousand place in the number 354,738 is 7 and it is greater than or equal to 5. This ultimately implies that, we would round up the number 4 to 5.

354,738 ≈ 355,000.

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1/13 = 0.0769 = 7.7%

9/26 = 0.346 = 34.6%

5/26 = 0.192 = 19.2%

1 mile = 1.6 kilometers

 multiply 40 mph by 1.6 = 64

car's rate = 64 kilometers per hour

multiply kilometers per hour by 4 = 256

 car will travel 256 kilometers in 4 hours

Answer:

Which equation represents the scenario?

✔ 6.25x + 12 = 30.75

How many people went to the movies?

✔ 3

Step-by-step explanation:

1. There are 3 peoples go to the movie.

2. The equation to represent the scenario is,

⇒ 6.25x + 12 = 30.75

Where, x is number of people.

What is an expression?

Expression in math is defined as the collection of the number, variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that;

The price of a ticket = $6.25

As a group, they spend $12 on refreshments.

Total spent money = $30.75

Now,

Let number of people go to the movie = x

Then, Total price spent on ticket = $6.25x

And, As a group, they spend $12 on refreshments.

So, Total spent money is equal to $30.75, as;

$6.25x + $12 = $30.75

This equation represents the scenario.

Now, Solve the equation for number of people as;

$6.25x + $12 = $30.75

Subtract 12 both side,

6.25x + 12 - 12 = 30.75 - 12

6.25x = 18.75

Divide by 6.25,

x = 3

Thus, There are 3 peoples go to the movie.

Therefore,

1. There are 3 peoples go to the movie.

2. The equation to represent the scenario is,

⇒ 6.25x + 12 = 30.75

Where, x is number of people.

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We know that Richard can apply fertilizer to 4485 square feet = 3/4 hour

To solve this problem, one approach is to find 1/4 then multiply by 4 to get the whole 4/4 or 1 hour.

So the solution would be:

4485/3=1495
Then multiply this by 4.

1495 multiplied by 4 is equal to 5980 square feet.

So Richard can apply fertilizer to 5980 square feet in 1 hour.

m∠PTS and m∠RTQ are vertically opposite angles thus both will be the same so the measure of m∠PTS will be 55°.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

Angle is shown by the sign ∠

Given the line segments, PQ and SR is intersecting at T

Thus m∠PTS and m∠RTQ will be vertically opposite angles

m∠PTS = m∠RTQ

Given that,

m∠PTS = 11(y - 10)

m∠RTQ  = 4y - 5

11(y - 10) = 4y - 5

11y - 110 = 4y - 5

11y - 4y = -5 + 110

7y = 105

y = 15

Therefore m∠PTS = 11(15 - 10)

m∠PTS = 55°

Hence "m∠PTS and m∠RTQ are vertically opposite angles thus both will be the same so the measure of m∠PTS will be 55°".

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