A square pyramid and a cube have the same volume if the length of each side of the base of the square pyramid is 2 cm in the height of the cube is 4 cm what is the height of the pyramid

a 8cm
b 16cm
c 24cm
d 48 cm

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: 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.

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.

Learn more about Volume here:
https://brainly.com/question/1578538

#SPJ2

Answer:

Both equations has different slope , so the system of equation have one unique solution.

Step-by-step explanation:

[tex]2x+y=4[/tex] , [tex]2y=6-2x[/tex]

To determine that the system of equation has unique solution, we need to find out the slope.

To find slope, we write the equation in the form of y=mx+b

Where m  is the slope and b is the y intercept

[tex]2x+y=4[/tex]

Subtract 2x on both sides

[tex]y=-2x+4[/tex]

here, m= -2 is the slope

[tex]2y=6-2x[/tex]

Divide both sides by 2

[tex]y=3-x[/tex]

[tex]y=-x+3[/tex]

Slope m = -1

Both equations has different slope , so the system of equation have one unique solution.

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].

Learn more:

1. Problem on decrease in the chances of an alcohol overdose: https://brainly.com/question/6391303

2. Problem on algebraic expression for the word phrase: https://brainly.com/question/1600376

3. Problem on comparing the value of digits: https://brainly.com/question/120717

Answer details:

Grade: College

Subject: Mathematics

Chapter: Probability

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

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.

To learn more on angle click:

brainly.com/question/28451077

#SPJ3

Answer:

Your Answer will be

-4/5   ,   -1/14    , 7/9

GradPoint Answer

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

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ3

The system of equations x + 3y = 0 and 9y = -3x is actually the same line, therefore there are an infinite number of solutions since the equations represent the same line with a slope of -3 and y-intercept of 0.

The student has given the linear equations x + 3y = 0 and 9y = -3x. To determine how many solutions this system has, we need to normalize the second equation. If we divide the second equation by 9, we get y = -\frac{1}{3}x, which, when reorganized, becomes x + 3y = 0. These two equations are actually the same line. In other words, every solution of the first equation is also a solution of the second equation, and vice versa.

Therefore, the system of equations has an infinite number of solutions because the lines represented by these equations overlap; they are the same line. This is an example of a dependent system where both equations represent the same relationship between x and y. In graph terms, the slope (m) of both lines is -3, and their y-intercept (b) is 0. This is evident from both the algebraic expression of the equations and from their graphical representation.

The system of equations has one solution.

The given system of equations is:

x + 3y = 0

9y = -3x

To solve this system, we can use the second equation to express y in terms of x.

Dividing both sides of the second equation by 9, we get:

y = (-3/9)x

Simplifying, we have:

y = (-1/3)x

We can observe that the equations of the lines represented by both equations in the system have the same slope, which is -1/3.

Since the lines have the same slope but different y-intercepts (0 for the first equation and 0 for the second equation), they will intersect at exactly one point, resulting in one solution for the system of equations.