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Final answer:

To find the per capita debt in 2005, divide the national debt of $10 trillion by the U.S. population of 100 million. The per capita debt comes out to be approximately $100,000 per person.

Explanation:

To calculate the per capita debt, we need to divide the national debt by the population of the U.S. The question states that the national debt at the end of 2005 was about $10 trillion, and the population was about 10 to the 8th power (100,000,000). To find the per capita debt, we perform the following calculation:

Per Capita Debt = Total National Debt / Population

= $10,000,000,000,000 / 100,000,000

= $100,000

Thus, the per capita debt was approximately $100,000 per person at the end of 2005.

Answer:

0.18173219.

Step-by-step explanation:

We have been asked to find what will be the probability that at least 6 of 9 adults use their smartphones in meetings or classes.

We will find our answer using Bernoulli's trails.

[tex]_{r}^{n}\textrm{c}\cdot p^{r}\cdot (1-p)^{n-r}[/tex]

First of all we will find the probabilities when r is 6, 7,8 and 9 then we will add them all.

When r=6,

[tex]_{6}^{9}\textrm{c}\cdot 0.46^{6}\cdot (1-0.46)^{9-6}[/tex]

[tex]\frac{9!}{6!3!} *0.46^{6} *0.54^{3}[/tex]

[tex]\frac{9*8*7*6!}{6!*3*2*1} *0.009474296896*0.157464[/tex]

[tex]84*0.009474296896*0.157464=0.12532[/tex]

Similarly we will find Probabilities when r=7, 8 and 9.

When r=7

[tex]_{7}^{9}\textrm{c}\cdot 0.46^{7}\cdot (1-0.46)^{9-7}[/tex]

[tex]\frac{9!}{7!2!} *0.46^{7} *0.54^{2}[/tex]

[tex]\frac{9*8*7!}{7!*2*1} *0.00435817657216*0.2916[/tex]

[tex]36*0.00435817657216*0.2916=0.04575039[/tex]

When r=8

[tex]_{8}^{9}\textrm{c}\cdot 0.46^{8}\cdot (1-0.46)^{9-8}[/tex]

[tex]\frac{9!}{8!1!} *0.46^{8} *0.54[/tex]

[tex]\frac{9*8!}{8!*1!} *0.00200476*0.54[/tex]

[tex]9 *0.00200476*0.54=0.0097431336[/tex]

When r=9,

[tex]_{9}^{9}\textrm{c}\cdot 0.46^{9}\cdot (1-0.46)^{9-9}[/tex]

[tex]\frac{9!}{9!0!} *0.46^{9} *1[/tex]

[tex]1 *0.00092219*1=0.00092219[/tex]

Now let us add all the probabilities to get the final answer.

[tex]0.12532+0.04575+0.00974+0.00092219=0.18173219[/tex]

Therefore, probability that at least 6 of 9 adults use their smartphones in meetings or classes is 0.18173219.

The probability that at least [tex]6[/tex] out of [tex]9[/tex] adult use their smartphone in meeting or classes is [tex]\fbox{\begin\\\ 0.1817\\\end{minispace}}[/tex].

Further explanation:

It is given that [tex]46\%[/tex] smartphone user use their smartphone in meetings or classes and at least [tex]6[/tex] out of [tex]9[/tex] adult smartphone user are selected randomly.

Here we will use the concept of Binomial probability.

If an experiment is performed [tex]n[/tex] times and it has only two outcomes that is, “success” and “failure”.So, the probability associated with this experiment is called Binomial probability.

The probability to get exactly [tex]r[/tex] successes in [tex]n[/tex] trial is given as follows,

[tex]\boxed{P=^{n}C_{r}p^{r}(1-p)^{n-r}}[/tex] ......(1)

Here, [tex]P[/tex] is the probability of [tex]r[/tex] successes in [tex]n[/tex] trials.

About [tex]46\%[/tex] smartphone user use their smartphone in meetings or classes that means the probability of the smartphone user use their smartphone in meetings or classes is as follows:

[tex]\begin{aligned}46\%&=\dfrac{46}{100}\\&=0.46\end{aligned}[/tex]

The statement, “at least six smartphone user” means six or more smartphone user. We will calculate the probability of the [tex]6,7,8[/tex] and [tex]9[/tex] adult smartphone user.

Substitute [tex]0.46[/tex] for [tex]p[/tex], [tex]9[/tex] for [tex]n[/tex] and [tex]6,7,8,9[/tex] for [tex]r[/tex] in equation (1) to obtain the probability of summation as follows,

[tex]P=^{9}C_{6}(0.46)^{6}(1-0.46)^{9-6}+^{9}C_{7}(0.46)^{7}(1-0.46)^{9-7}+^{9}C_{8}(0.46)^{8}(1-0.46)^{9-8}+\qquad^{9}C_{9}(0.46)^{9}(1-0.46)^{9-9}\\\\P=\dfrac{9!}{6!\cdot(9!-6!)}\cdot(0.46)^{6}\cdot(0.54)^{3}+\dfrac{9!}{7!\cdot(9!-7!)}\cdot(0.46)^{7}\cdot(0.54)^{2}+\dfrac{9!}{8!\cdot(9!-8!)}\cdot(0.46)^{8}\cdot(0.54)^{1}+\dfrac{9!}{9!\cdot(9!-9!)}\cdot(0.46)^{9}\cdot(0.54)^{0}[/tex]  

Further solving the above equation as follows,  

[tex]\begin{aligned}P&=84\cdot(0.46)^{6}\cdot(0.54)^{4}+36\cdot(0.46)^{7}\cdot(0.54)^{2}+9\cdot(0.46)^{8}\cdot(0.54)^{1}+1\cdot(0.46)^{9}\cdot(0.54)^{0}\\&=0.1253+0.04575+0.009743+0.00092219\\&=0.1817\end{aligned}[/tex]  

Therefore, the probability that at least [tex]6[/tex] out of [tex]9[/tex] adult use their smartphone in meeting or classes is [tex]\boxed{0.1817}[/tex].

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Answer details:

Grade: College

Subject: Mathematics

Chapter: Probability

Keywords:  Probability, numbers, chances, smartphone, meeting, classes, 0.1817, summation, user, equation, selected, Binomial probability, randomly.

The locker is closer.

The required height of the pyramid is 6 inches.

Given that,

A triangular pyramid has a volume of 840 cubic inches a triangular base has a base length of 20 inches and a height of 21 inches find the height of the pyramid is to be determined.

Volume is defined as the ratio of the mass of an object to its density. In other words, the Volume of the object is the product area of the cross-sectional profile and extruded height.

Here,
The base area of the triangle = 20 * 21 = 420 inches².

Volume of the triangular pyramid = 1 / 3 * base area * height
840 = 1 / 3  * 420 * height
840 / 140 = height
height = 6 inch.

Thus, the required height of the pyramid is 6 inches.

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Answer:

I also got 43 using the same strategy as the first guy.

Step-by-step explanation:

90*-40*=43*

67° and 23° are complementary angles.

67 + 23 = 90

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

We know that, a ray is a line that continues on forever inn one direction with a point at it's start.

here, we have,

67 degrees and 23 degrees

we know,

67 + 23 = 90

Hence, 67° and 23° are complementary angles.

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Answer:

2 and 2 over 3 is the Correct Answer

Step-by-step explanation:

I took the test and got the question wrong, I thought it was 3/8 but it wasnt, my test said the correct answer was 2 and 2 over 3 so I hope you get it right even though I didnt :)

The solution of the expression is,

⇒ a = 3 / 8

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 1 over 4a = 2 over 3.

Now, We can simplify as;

⇒ `1 / 4a = 2 / 3

⇒ 3 = 2 x 4a

⇒ 3 = 8a

⇒ a = 3 / 8

Thus, The solution of the expression is,

⇒ a = 3 / 8

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Answer:

20 million cubic feet every 1 mins

Step-by-step explanation:

180÷3=60

60÷3=20

The area for carpeting a floor is the measurement of the surface that needs to be covered by carpet, while the perimeter refers to the total length around the edges of the floor.

The area for carpeting a floor is the measurement of the surface that needs to be covered by carpet. The perimeter, on the other hand, refers to the total length around the edges of the floor. The choice between calculating the area or perimeter for carpeting a floor depends on whether you need to determine how much carpet material is needed (area) or how much carpet edge is required (perimeter).

For example, if you want to calculate the area to determine the amount of carpet needed to cover the floor, you would measure the length and width of the floor and multiply them together. The resulting area would be in square units (such as square feet or square meters).

On the other hand, if you want to calculate the perimeter to determine how much carpet edge needs to be trimmed or finished, you would add up the lengths of all the sides of the floor. The resulting perimeter would be in linear units (such as feet or meters).

In comparing distances, Lynne lives closer to the playground than Jorge. This is determined by comparing the fractions representing their distances from the playground, with Lynne's being smaller.

In this situation, we need to compare the distances each person lives from the playground. Jorge lives 5/6 mile from the playground and Lynne lives 4/6 mile from the playground. Since a smaller fraction represents a smaller distance, we can say that Lynne lives closer to the playground than Jorge does.

To understand this better, consider fractions as a way to divide a whole into parts. The larger the denominator, the more parts the whole is divided into and the smaller each part is. But in this case, the denominators are the same (6), so we look at the numerators. The numerators tell us how many of these parts we have. Since 4 is smaller than 5, Lynne who lives 4/6 mile away lives closer than Jorge who lives 5/6 mile away.

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Answer: CO≅HZ

Step-by-step explanation:

The two chords are congrunt so the intercepted arcs are congruent  CO≅HZ

Since segment CO is congruent to segment HZ, a congruence statement that is true include the following: C. CO ≅ HZ.

In Mathematics and Euclidean Geometry, two geometric figures are considered to be congruent only when their corresponding side lengths are equal and the magnitude of their angles are congruent.

Since we know that rigid motions preserve both the side length and angle measure, this ultimately implies that congruent segments have the same (equal) length.

In this context, we can reasonably infer and logically deduce that arc CO is congruent with arc HZ because chord CO is congruent to chord HZ;

arc CO ≅ arc HZ (intercepted arcs).

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Answer:

The decimal point should be placed between the digits 7 and 6 because the product should be greater than 4 × 1 and less than 5 × 2.

Step-by-step explanation:

Answer: The mean hours the groups of teens spent studying is little bit greater for  15- to 16-year old teen or about same .

The range range for the two groups of of teens is greater for 13- to 14-year old teens.

Step-by-step explanation:

We know that the mean of a data is given by :-

[tex]\text{Mean}=\dfrac{\text{Sum of all observations}}{\text{Number of observations}}[/tex]

Range = largest observation - least observation

From the given table :

The mean hours spent by 13- to 14-year olds is given by :-

[tex]\text{Mean}=\dfrac{87}{10}=8.7[/tex]

[tex]\text{Range=12-2=10}[/tex]

The mean hours spent by 15- to 16-year olds is given by :-

[tex]\text{Mean}=\dfrac{89}{10}=8.9[/tex]

[tex]\text{Range=12-4=8}[/tex]

The mean hours the groups of teens spent studying is little bit greater for  15- to 16-year old teen or can say about same.

The range range for the two groups of of teens is greater for 13- to 14-year old teens.