A train leaves the station every 12 minutes, a train leave the station every 18 minutes, at 8am a bus and a train leave the station at the same time, when is the next time the bus and train will leave at the same time

The statement that involves descriptive statistics is -

Option A) The Alcohol, Tobacco, and Firearms Department reported that Houston had 1,791 registered gun dealers in 1997.

What are two categories of field statistics?

There are two categories of field statistics. Descriptive and inferential statistics. Both of them help analysts to make sense of row after row data.

Descriptive statistics presents quantifiable descriptions in a simple way. Inferential statistics is used to draw conclusions that go beyond the raw data only. It is used in making judgments, inferences to deeper general conditions.

The Alcohol, Tobacco, and Firearms Department reported that Houston had 1,791 registered gun dealers in 1997.

Descriptive statistics are useful in describing the basic features of the data being analyzed. They simply provide what the raw data shows. They simplify huge amounts of data sensibly and make it presentable in a manageable form.

With regard to the question, raw data is available stating that the registered gun dealers were 1791 in 1997. It, therefore, involves descriptive statistics.

Therefore, the correct answer is option A.

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Which of the following statements involve descriptive statistics as opposed to inferential statistics?

A) The Alcohol, Tobacco, and Firearms Department reported that Houston had 1,791 registered gun dealers in 1997.

B) Based on a survey of 400 magazine readers, the magazine reports that 45% of its readers prefer double-column articles.

C) The FAA samples 500 traffic controllers in order to estimate the percent retiring due to job-stress-related illness.

D) Based on a sample of 300 professional tennis players, a tennis magazine reported that 25% of the parents of all professional tennis players did not play tennis.

Type I error is "Megan's results show significant improvements in health associated with a whole foods diet."

A Type I error occurs when the null hypothesis is rejected, even though it is true.

In this case, the null hypothesis states that a whole foods diet would not have any impact on general health.

Therefore, a Type I error would occur if Megan's results show significant improvements in health associated with a whole foods diet.

This means that Megan would reject the null hypothesis and conclude that a whole foods diet does have an impact on general health, even though it is not true.

So, the statement that would indicate a Type I error is "Megan's results show significant improvements in health associated with a whole foods diet."

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The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

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The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

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Answer:

7:12

Step-by-step explanation:

boys=5

girls=7

total=boys+girls

12=5+7

girls:total

7:12

Answer:

Annette should plan to spend 2.25 hours walking back.

Step-by-step explanation:

To solve this problem, we can use the formula:

Time = Distance / Speed

Let's assume the distance of the race is D miles.

Annette spends her time running the distance of the race, which takes:

Time running = D / 9 hours

She then walks back the same distance, which we need to find the time for:

Time walking = D / 3 hours

Since Annette has a total of 3 hours for her training, the sum of the running time and walking time should equal 3 hours:

D / 9 + D / 3 = 3

To simplify the equation, we can multiply all terms by 9 to eliminate the denominators:

D + 3D = 27

Combining like terms:

4D = 27

Dividing both sides of the equation by 4:

D = 6.75

So, the distance of the race is 6.75 miles.

To find the time Annette should spend walking back, we substitute the distance into the time-walking formula:

Time walking = D / 3 = 6.75 / 3 = 2.25 hours

Therefore, Annette should plan to spend 2.25 hours walking back.

Answer:

  b = 20

Step-by-step explanation:

This is a right triangle with the ratio of the given sides being ...

  15 : 25 = 3 : 5

This means it is a 3:4:5 right triangle. The side ratios are ...

  a : b : c = 3 : 4 : 5 = 15 : 20 : 25

The missing side length is b = 20.

__

You can also figure this using the Pythagorean theorem.

  c² = a² + b²

  25² = 15² +b²

  625 -225 = b² = 400

  b = √400 = 20

The missing side length is 20.

Answer:

b)

Step-by-step explanation:

a) 4+12>8

12+8>4

4+8=12

NO

b) 5+12>10

10+5>12

12+10>5

YES

c) 16+4>6

6+4<16

NO

d) 30+12>6

12+6<30

NO

Answer:

A, y= -6x + 2

Step-by-step explanation:

1. Put the equation into slope intercept form

6y = 9 - x

y= -1/6x + 9/6

The slope of equation 1 is -1/6

2. A perpendicular line is the inverse slope of our firsy equation. (-1/6)^-1 = -6.

3. The y intercept of a line in slope intercept form is the b value in the equation as written:

y=mx+b

Therefore, if m=-6 and b=2, our equation is

y= -6x + 2

Answer: 3/4

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 12 and 16 is 4

Divide both the numerator and denominator by the GCD

12 ÷ 4

16 ÷ 4

Reduced fraction: 3/4

Therefore, 12/16 simplified to lowest terms is 3/4.

Answer:.

Step-by-step explanation:

Answer and step-by-step explanation:

The polar form of a complex number \(a+ib\) is the number \(re^{i\theta}\) where \(r = \sqrt{a^2+b^2}\) is called the modulus and \(\theta = tan^-^1 (\frac ba)\) is called the argument. You can switch back and forth between the two forms by either remembering the definitions or by graphing the number on Gauss plane. The advantage of using polar form is that when you multiply, divide or raise complex numbers in polar form you just multiply modules and add arguments.

(a) let's first calculate moduli and arguments

\(r_1 = \sqrt{(-2\sqrt3)^2+2^2}=\sqrt{12+4} = 4\\ \theta_1 = tan^-^1(\frac{2}{-2\sqrt3}) =-\pi/6\\r_2=\sqrt{1^2+1^2}=\sqrt2\\ \theta_2 = tan^-^1(\frac 11)= \pi/4\)

now we can write the two numbers as

\(z_1=4e^{-i\frac \pi6}; z_2=e^{i\frac\pi4}\)

(b) As noted above, the argument of the product is the sum of the arguments of the two numbers:

\(Arg(z_1\cdot z_2) = Arg(z_1)+Arg(z_2) = -\frac \pi6 + \frac \pi4 = \frac\pi{12}\)

(c) Similarly, when raising a complex number to any power, you raise the modulus to that power, and then multiply the argument for that value.

\((z_1)^1^2=[4e^{-i\frac \pi6}]^1^2=4^1^2\cdot (e^{-i\frac \pi6})^1^2=2^2^4\cdot e^{-i(12)\frac\pi6}\\=2^2^4 e^{-i\cdot2\pi}=2^2^4\)

Now, in the last step I've used the fact that \(e^{i(2k\pi+x)} = e^i^x ; k\in \mathbb Z\), or in other words, the complex exponential is periodic with \(2\pi\) as a period, same as sine and cosine. You can further compute that power of two with the help of a calculator, it is around 16 million, or leave it as is.

Answer:

what is your question?

Step-by-step explanation:

The range of the graph of the exponential function is (b) {y | y > 0}

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

The graph of the exponential function

The rule of an exponential function is that

The domain is the set of all real numbers

This means that the input value can take all real values

However, the range is always greater than the constant term

From the graph, the constant term is 0

So, the range is y > 0

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Answer:

1st term= -3

Step-by-step explanation:

You are already given an expression for nth term

so all you do is plug in 1 for n to get the first term and so forth

t=7(1) -10

t=7-10

t=-3

The matrix 3A + B cannot be defined, as 3A and B have different dimensions, hence they cannot be added.

When we add two matrices, we add the equivalent elements, that is, the elements at the same position in each matrix, hence for the addition of matrices they should have the same dimensions.

The matrices are given by:

3a: 3[5 2]' = [15 6].

b = [7 1;5 0].

With the ; indicating a new line, hence they have different dimensions(A 2 x 1 and B 2 x 2), so the matrix 3A + B cannot be defined.

Therefore, the matrix 3A + B cannot be defined, as 3A and B have different dimensions, hence they cannot be added.

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Answer:

Step-by-step explanation:

Solve for x.

2x + 9 = 33

2x = 24

x = 12

A. x = 7.5

B. x = 12

C. x = 21

D. x = 84

Answer:

\(2x + 9 = 33 \\ 2x = 33 - 9 \\ 2x = 24 \\ x = \frac{24}{2} \\ x = 12\)

Answer:

Step-by-step explanation:

ASHY is the square with the side of 5.

DYES is the rhombus since all sides are same and diagonals are perpendicular.

The area of the rhombus is the difference of the area of the big square and the sum of small squares and triangles:

Answer:

15 square units

Step-by-step explanation:

its correct, trust me

Solution

Step 1

Two distinct lines intersecting each other at 90° or at right angles are perpendicular to each other.

Hence apply this to question 8 the type of lines shown in the figure is perpendicular lines. Option C

Step 2

To explain this as stated above line A and line B intersect each other at a right angle hence line A and B are perpendicular lines. The line segments are seen below.

Answer:

If g(x) = f(x) + k, what is the k value?

The answer The value of k is 6

Answer:

0.7788 = 77.88% probability that more than three customers arrive in 10 minutes

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

\(f(x) = \mu e^{-\mu x}\)

In which \(\mu = \frac{1}{m}\) is the decay parameter.

The probability that x is lower or equal to a is given by:

\(P(X \leq x) = \int\limits^a_0 {f(x)} \, dx\)

Which has the following solution:

\(P(X \leq x) = 1 - e^{-\mu x}\)

The probability of finding a value higher than x is:

\(P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}\)

In this question, we have that:

The time between arrivals of customers at an automatic teller machine is an exponential random variable with a mean of 4 minutes, and we have three customers, which means that \(m = 3*4 = 12, \mu = \frac{1}{12} = 0.0833\)

(a) What is the probability that more than three customers arrive in 10 minutes

This is P(X > 3). So

\(P(X > 3) = e^{-0.0833*3} = 0.7788\)

0.7788 = 77.88% probability that more than three customers arrive in 10 minutes

Answer:

(-1,1)

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

equation form:
x=-1, y=1

have a great day and thx for your inquiry :)

By substituting each of the provided options into the given system of linear equations, it is revealed that the ordered pair (-1, 1) is a valid solution for both the equations.

The correct answer is (-1, 1)

In mathematics, a system of linear equations consists of multiple linear equations with the same variables. These equations describe various relationships among these variables, typically representing lines in a multi-dimensional space. Solving such systems involves finding values for the variables that satisfy all equations simultaneously. Methods like substitution, elimination, or matrix algebra can be used to solve these systems. These systems are fundamental in fields like physics, engineering, economics, and computer science for modeling and solving real-world problems involving multiple interconnected variables.

We can solve this problem by substituting values from the given options into the equations and checking for which option both equations are valid. The system of linear equations is: x + 4y = 3 and y = -4x - 3.

Therefore, the ordered pair that is a solution to the system of linear equations is (-1, 1).

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Answer:

18 Bowls of Candy

Step-by-step explanation:

Camila has 6 bags of candy, and she can pour 1/3 of a bag into a bowl. To determine how many bowls of candy she can make in total, we need to divide the total amount of candy by the amount of candy per bowl.

Since Camila can pour 1/3 of a bag into a bowl, it means she can make 3 bowls of candy with a full bag.

Now, we can calculate the total number of bowls of candy:

Total bowls of candy = (Number of bags) x (Bowls per bag)

Total bowls of candy = 6 bags x 3 bowls per bag

Total bowls of candy = 18 bowls

Therefore, Camila can make a total of 18 bowls of candy with her 6 bags of candy.

Hi

500 *1.025^10 ≈ 640.04

The real engine is 65.25 feet long

The scale is given as:

Scale = 87 feet to 1 foot

The scale length is given as

Scale length = 9 inches

Convert inches to feet

Scale length = 9/12 feet

The actual length is then calculated as:

Actual = 87 * 9/12 feet

Evaluate

Actual = 65.25 feet

Hence, the real engine is 65.25 feet long

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Answer:

41832

Step-by-step explanation:

Table

Number of donuts Price

1 $1.05

2 $ 2.1

3 $3.15

4 $4.2

5 $5.25

6 $6.3

10 $10.5

slope = (10.5 - 1.05) / 10 - 1

= 9.45 / 9

= 1.05

Equation

y - 10.5 = 1.05 (x - 10)

y = 1.05x - 10.5 + 10.5

y = 1.05x

For 40 donuts

y = 1.05(40)

y = $42

Solve for x by simplifying both sides of the equation, then isolating the variable.

x=−2

hope this is what your looking for

Answer:

x = -2

Step-by-step explanation:

\(-4+x=\frac{3}{4}x-\frac{9}{2}\)

\(\mathrm{Add\:}4\mathrm{\:to\:both\:sides}\)

\(-4+x+4=\frac{3}{4}x-\frac{9}{2}+4\)

\(Simplify\)

\(x=-\frac{1}{2}+\frac{3}{4}x\)

\(\mathrm{Subtract\:}\frac{3}{4}x\mathrm{\:from\:both\:sides}\)

\(x-\frac{3}{4}x=-\frac{1}{2}+\frac{3}{4}x-\frac{3}{4}x\)

\(\frac{1}{4}x=-\frac{1}{2}\)

\(\mathrm{Multiply\:both\:sides\:by\:}4\)

\(4\cdot \frac{1}{4}x=4\left(-\frac{1}{2}\right)\)

\(x=-2\)

~lenvy~