Explain how you can determine that the following system has one unique solution – without actually solving the system. 2x+y=4 , 2y=6-2x

Answer:

[tex][2, 7][/tex]

Step-by-step explanation:

5 + p = 2p + 3

- 2p - 2p

______________

5 - p = 3

-3 - 3

________

2 - p = 0

-2 - 2

________

-p = -2

2 = p [Plug this back into both equations above to get the n-term of 7]; 7 = p

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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:

Step-by-step explanation:

A tube has a radius of a 9 inches and a height of 7 inches. What's its approximate volume

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:

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.

To find the number of 1/3 cups of flour Chris needs, we need to divide the total amount of flour needed by the amount that can be measured with the 1/3 cup measuring cup. In this case, Chris needs 28 1/2 cups of flour.

To find the number of 1/3 cups of flour Chris needs, we need to divide the total amount of flour needed (3 1/2 cups) by the amount that can be measured with the 1/3 cup measuring cup.

To do this, we convert the whole number 3 to thirds by multiplying by 3, which gives us 9 thirds. Then we add the 1/2 cup, which is equivalent to 3/6 or 6/12. So, the total amount in thirds is 9 + 6/12 = 9 1/2 thirds.

Now, we divide the total number of thirds by the number of thirds in one 1/3 cup.

9 1/2 thirds ÷ 1/3 third/cup = (9 1/2) ÷ (1/3) = (19/2) ÷ (1/3) = 19/2 × 3/1 = 19/2 × 3/1 = 57/2 = 28 1/2 cups.

Answer:

Your Answer will be

-4/5   ,   -1/14    , 7/9

GradPoint Answer

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.