Divide the following numbers in scientific notation and express the result in scientific notation.

The solution of the system of linear equations has infinitely many solutions.

Linear equation is defined as an algebraic equation of the form y=mx + b. involving only a constant and a first-order term, where m is the slope and b is the y-intercept.

Here we have given that the following linear equations are given then are listed as follows:

x + y = 4

y + z = 4

x + z = 4

ax + by + cz = 0

Here we have know that the  sub-system consisting of 3 first equations has a unique solution x = y = z = 2.

While we add the fourth equation, then it becomes look like as follows:

=> 2a + 2b + 2c = 0

When we simplify this one then we get,

=> a + b + c = 0.

Which means that if  a + b + c = 0,   then the system of 4 equations has a unique solution otherwise it is IMPOSSIBLE to this system to have infinitely many solutions.

Complete Question:

Try to find values of a, b, and c (if possible) such that the system of linear equations has a unique solution, no solution, and infinitely many solutions. (If not possible, enter IMPOSSIBLE.)

x + y = 4

y + z = 4

x + z = 4

ax + by + cz = 0

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The angle θ of thread deflection in the extreme position is given by tan^−1(2).

The angle of thread deflection in the extreme position can be calculated by using the equation of motion of a simple pendulum.

The equation of motion for a simple pendulum is given by m g L sinθ = m a. Here, m is the mass of the ball, g is the gravitational acceleration, L is the length of the thread and θ is the angle of the thread.

From the given condition, the acceleration of the ball in the extreme and lowest positions are equal. This implies that the acceleration of the ball in the extreme position is equal to the acceleration due to gravity.

Therefore, the equation of motion reduces to g L sinθ = g. Solving for θ, we get sinθ = 1, which implies that θ = tan^−1(2).

Therefore, the angle θ of thread deflection in the extreme position is given by tan^−1(2).

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If there is sufficient evidence to reject the null hypothesis, we conclude that the alternate hypothesis is true. if there is not sufficient evidence to reject the null hypothesis, we conclude that the null hypothesis might be true, but we never conclude that the null hypothesis is true

if there is not sufficient evidence to reject the null hypothesis, we conclude that the null hypothesis might be true, but we never conclude that the null hypothesis is true

This statement is describing the process of hypothesis testing in statistics. In hypothesis testing, a null hypothesis is a statement that there is no significant difference between two sets of data or no relationship between two variables. An alternate hypothesis is a statement that there is a significant difference or relationship.

When conducting a hypothesis test, a researcher will collect data and use statistical methods to determine the likelihood that the null hypothesis is true given the data. If the likelihood is low, the researcher will reject the null hypothesis and conclude that the alternate hypothesis is true. If the likelihood is high, the researcher will fail to reject the null hypothesis, but this does not necessarily mean that the null hypothesis is true. It means that the data is not strong enough to reject the null hypothesis.

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Answer:

a)  Exponential growth function: 60%

b)  Exponential decay function: 20%

c)  Neither

d)  Exponential decay function: 45%

Step-by-step explanation:

[tex]\textsf{Exponential Growth}: \quad y=a(1+r)^x[/tex]

[tex]\textsf{Exponential Decay}: \quad y=a(1-r)^x[/tex]

where:

Given function:

[tex]f(x) = 0.3(1.6)^x[/tex]

The function is an exponential growth function and the growth rate is:

[tex]1+r=1.6 \implies r= 0.6 = 60\%[/tex]

Given function:

[tex]g(x) = 0.8^{0.5x} - 7[/tex]

The function is an exponential decay function and the decay rate is:

[tex]1-r=0.8 \implies r=0.2=20\%[/tex]

Given function:

[tex]h(x) = 3(-5)^x[/tex]

This is neither an exponential growth or decay function as exponential functions cannot have negative bases.

Natural base exponential function

[tex]y=ae^{rx}[/tex]

If a > 0 and r > 0, the function is an exponential growth function.

If a > 0 and r < 0, the function is an exponential decay function.

Given function:

[tex]f(x) = e^{-0.45x} + 4[/tex]

As a = 1 > 0 and r = -0.45 < 0, the function is exponential decay function and the decay rate is:

[tex]r=-0.45=45\%[/tex]

There are 94830 integers greater than 5400

At first, go it looks .like an infinite number but As digits are distinct

so a maximum 10 digits number is possible

but 2 & 7 can not be used so the maximum 8-digit number can be there

Total number = 4 digits numbers, 5 Digits numbers, 6 digits number, 7 digits numbers, 8 digits numbers

All the 5 - 8 digit numbers would  be > 5400

Available number of Digits = 8  ( 0, 1, 3, 4, 5, 6, 8, 9)

for numbers greater than 4 digits (5 - 8 Digits),  1st  digit can be  1, 3, 4, 5, 6, 8, 9 then from the 2nd digit onward 0 can also be a digit but the already used digit can not be used. and further one digit (already used) will keep reducing

5  Digits numbers = 7 * 7 * 6  * 5 * 4  = 5880

6 Digit Numbers =  7 * 7 * 6  * 5 * 4 *3 =  17640

7  Digits numbers = 7 * 7 * 6  * 5 * 4*2  = 35280

8 Digit Numbers =  7 * 7 * 6  * 5 * 4 *3*2*1 =  35280

Now in 4-digit numbers

Number starting with 6, 8, 9   > 5400   & number starting with 5

Number starting with 6 , 8 , 9 = 3 * 7 * 6 * 5 = 630

Number starting with 5, the second digit must be 4, 6, 8, 9

Number starting with 5 = 1 * 4* 6 * 5 = 120

Total integers greater than 5400

=5880 + 17640 + 35280 + 35280 + 630 + 120

= 94830

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This is a True statement that both the matrix equation and the augmented matrix translate into the same system of linear equations.

What are Linear equations?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.

A rectangular matrix is a grouping of numbers into rows and columns. Systems of equations can be solved using matrices. But first, we need to understand how to use matrices to represent systems.

An augmented matrix can be used to express a set of equations. Each column in an augmented matrix represents a variable or the constant terms, and each row in an augmented matrix represents one equation in the system. As a result, it is clear that augmented matrices provide a convenient approach to express systems of equations.

Therefore it is true that the solution set of the equation's equation is the same as the solution set of the linear system whose augmented matrix is.

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Answer:

118

Step-by-step explanation:

18*4=72

8+3*2=22

8*3=24

72+22+24=118

For it to be parallel, the point must follow the translation from (2,7) to that point similar to (0, -3) to (-5, -5) which is left 5 and down 2. So left 5 and down 2 for (2, 7) makes it (-3, 5)

The answer is x4 = input.nextDouble() and double avgnumber = (x1 + x2 + x3 + x4) / 4.

Declare the double variables x1, x2, x3, and x4.
double x1, x2, x3, x4;
Read each variable from input in that order.
Scanner input = new Scanner(System.in);
System.out.println("Enter x1:");
x1 = input.nextDouble();
System.out.println("Enter x2:");
x2 = input.nextDouble();
System.out.println("Enter x3:");
x3 = input.nextDouble();
System.out.println("Enter x4:");
x4 = input.nextDouble();
To Find the average of x1, x2, x3, and x4 and assign the result to avgnumber.
double avgnumber = (x1 + x2 + x3 + x4) / 4;

//This code takes four double variables from input and calculates the average by adding the four numbers together and dividing by four. The result is stored in the double variable avgnumber.

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The formula for calculating the number of cards each player receives in Bridge is N/4, where N = number of cards in the deck.

For a standard deck of 52 cards, each player would receive 52/4 = 13 cards. This can be further simplified to 13.33, however, since cards cannot be divided, the result is rounded down to 13 cards. Therefore, each player in a Bridge game with a standard deck of 52 cards will receive 13 cards.

The total number of cards in the deck is 52, so each player will get 13 cards. This can be expressed mathematically using the formula P = 52/4, where P is the number of cards per player. Therefore, P = 13. We can also use the formula to calculate the number of players if we know the total number of cards. For example, if we have 156 cards, the number of players can be calculated using the formula P = 156/4, which gives us P = 39. Therefore, there will be 39 players in the game.

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The length of BC is 10.

When two triangles have some common corresponding properties, they are said to be similar. But they are no congruent.

In the given question, comparing triangles ABC and DEC. We have;

DE/ AB = EC/ BC

But,

BC = 2BE

     = 2x

So that,

(x + 2)/ (4x - 6) = x/ 2x

(x + 2)/ (4x - 6) = 1/ 2

2(x + 2) = (4x - 6)

2x + 4 = 4x - 6

collect like terms

6 + 4 = 4x - 2

10 = 2x

x = 10/ 2

x = 5

Then,

BC = 2x

     = 2*5

BC = 10

The length of BC is 10.

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The series discount of 20/10/10 means that there are three discounts given in sequence. The first discount is 20%, the second is 10%, and the third is 10%.

What does math's % mean?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

Let's call the original price x.

x - (20/100x) = 0.8x

then

0.8x - (10/1000.8x) = 0.72x

and finally

0.72x - (10/100*0.72x) = 0.648x

So, the net cost of $453.60 is equal to 0.648x.

We can find the original price by dividing the net cost by 0.648:

x = $453.60 / 0.648 = $700

So, the list price of the PC was $700.

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The correct unit fraction to multiply by the second term to create a common denominator is [tex](x+2)/(x+2)[/tex]

To find a common denominator for the given rational expression, we need to identify a unit fraction that can multiply the second term so the denominators of both terms will be the same.

The denominators of the two terms are [tex]x^2-4[/tex] and [tex]x-2[/tex]. To find a common denominator for these terms, we can multiply the second term  [tex](x+2)/(x+2)[/tex] which is a unit fraction because it is equal to 1.

Multiplying the second term by [tex](x+2)/(x+2)[/tex] gives us:

[tex](x 4)/(x-2) * (x+2)/(x+2) = (4x(x+2))/(x^2-4)[/tex]

Now both terms have a common denominator [tex]x^2-4[/tex]. Thus the correct unit fraction to multiply by the second term to create a common denominator is [tex](x+2)/(x+2)[/tex]

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150°

Because it is not acute it cant be 30°

The volume of one marble is 0.5 ml and the water level before dropping the marbles is 8 ml.

The volume of an object is the amount of space occupied by the object within all boundaries. The volume of any geometrical shape can be calculated by the respective formula.

The Water Displacement Method is a method that is used to calculate the volume of any object without knowing the dimensions. If we drop the object into the water and the amount that can be displaced will be equal to the volume of the object.

Here we have

After dropping 4 marbles, the height of the water level is 10 ml

After dropping 6 marbles, the height of the water level is 11 ml

This means for 2 extra marbles the water level increase up to 1 ml  

So, the Volume of the marble = 1 ml/2 = 0.5 ml

From the given data,

After dropping 4 marbles the water level is 10 ml

As we know the volume of 1 marble = 0.5ml

=> Volume of 4 marbles = 4 × 0.5ml = 2ml

The water level before dropping 4 marbles = 10 ml - 2 ml = 8 ml    

Therefore,

The volume of one marble is 0.5 ml and the water level before dropping the marbles is 8 ml.

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Answer:

The area of the ΔABC is 98 cm²

In a triangle, we can use the sine formula to find the area of the triangle when we know one angle and the two side lengths opposite and adjacent to that angle.

Area of ΔABC = (1/2) bc sinA

Substitute b = 28 cm, c = 14 cm, and m∠A = 30° into the formula:

Area of ΔABC = (1/2) × 28cm × 14cm × sin 30°

Area of ΔABC = 98 cm²

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Answer:

where is the table?

Step-by-step explanation:

repost it with a picture of the table so we can answer it or tell the details and I'll answer in the comments?

Answer:

2x-4x+2x=17-12-5

0x=0

what are you up for now and what time do you think you'll have time for

The value of X in the given system of matrix is,

[tex]X=\left[\begin{array}{ccc}\frac{-97}{145}&\frac{-45}{145} \\\\\frac{20}{29}&\frac{21}{29}\\\end{array}\right][/tex]

Matrices are one of the most powerful tools in mathematics. The evolution of the concept of matrices is the result of an attempt to obtain compact and simple methods of solving the system of linear equations.

We have 2 by 2 matrix in the form,

[tex]\left[\begin{array}{ccc}9&9\\-9&-9\\\end{array}\right] X+\left[\begin{array}{ccc}6&3\\7&9\\\end{array}\right] =\left[\begin{array}{ccc}-1&8\\-4&6\\\end{array}\right] X\\\\Assume, X=\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] \\\\[/tex]

After multiplication,

[tex]9a+9c+6=-a+8c\\\\-9a-9c+7=-4a+6c\\\\9b+9d+3=-b+8d\\\\-9b-9d+9=-4b-6d\\\\[/tex]

After solving the given system of equations

[tex]a=\frac{-97}{145}\\\\b=-\frac{54}{145}\\\\c=\frac{20}{29}\\\\d={21}{29}\\\\Hence, \\X=\left[\begin{array}{ccc}\frac{-97}{145}&\frac{-45}{145} \\\\\frac{20}{29}&\frac{21}{29}\\\end{array}\right][/tex]

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If a value of 48 was added, the median of the data-set would remain decay from 79.5 to 77.

The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than.

The ordered data-set for this problem is given as follows:

57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105.

The data-set has an even cardinality of 12, hence the median is the mean of the 6th and the 7th elements, as follows:

(77 + 82)/2 = 79.5.

A value of 48 would be lowest value of the data-set, the cardinality would be odd, and thus the middle value would be of 77.

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The outcome that are there when a six sided dice is rolled four times is 2

A sample space is a collection or a set of possible outcomes of a random experiment. The p space is represented using the symbol, “S”. The subset of possible outcomes of an experiment is called events. A sample space may contain a number of outcomes that depends on the experiment.

The sample space of getting a 6 from a die is 1. A die has six sides and are labelled 1-6

The outcome of 4 times is is 4

Therefore for two rolls, it will be 4/2 = 2

Therefore the outcome to get 6 exactly two times is 2.

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The formula used to explain this statement is known as Modus Tollens, which is a form of logical inference.

Modus Tollens states that if the antecedent (A) of a conditional statement is false, then the consequent (B) must also be false. This is expressed mathematically as ¬A ⟹ ¬B. The formula used to explain this statement is known as Modus Tollens, which is a form of logical inference.

In this particular example, A is the statement that Lewis is a famous author, and B is the statement that Lewis knows how to write. Since the statement A is false, the statement B must also be false. This can be represented mathematically as:

¬A ⟹ ¬B

¬(Lewis is a famous author) ⟹ ¬(Lewis knows how to write)

False ⟹ False

Therefore, Lewis does not know how to write.

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The row form of the system is 5x = 2 and y – y = 0.

Column form:

3x + y = 5

2x – y = –3

Row form:

3x + 2x = 5 – 3

y – y = 0

The row form of this system is 3x + 2x = 5 – 3 and y – y = 0. To convert from column form to row form, the first step is to eliminate the y terms in the equations. To do this, we need to add the two equations together. This gives us:

3x + y = 5

2x – y = –3

3x + 2x = 5 + (–3)

y – y = 0

5x = 2

y – y = 0

Finally, we can solve for x and y.

5x = 2  ⇒  x = 2/5

y – y = 0  ⇒  y = 0

Therefore, the row form of the system is 5x = 2 and y – y = 0.

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The probability that 8 or more of these students were classed at professional level is given as follows:

0%.

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The values of the parameters for this problem are given as follows:

n = 10, p = 0.05.

Hence the probability of 8 or more of these students were classed at professional level is given as follows:

P(X >= 8) = P(X = 8) + P(X = 9) + P(X = 10)

In which:

Hence the probability is of 0%.

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Answer: Liliana has 9 quarters and 27 nickels.

Step-by-step explanation:

Let's call the number of quarters Liliana has "q" and the number of nickels she has "n".

From the problem, we know that:

n = q + 18 (because she has 18 more nickels than quarters)

We also know that the total value of the coins is $3.60. We can use the following equation to find the total number of coins:

(0.25 * q) + (0.05 * n) = 3.60

Now we can substitute the first equation into the second equation to get:

(0.25 * q) + (0.05 * (q + 18)) = 3.60

Simplifying this equation:

0.25q + 0.05q + 0.90 = 3.60

0.30q = 2.70

q = 9

So Liliana has 9 quarters. We can use the first equation (n = q + 18) to find the number of nickels she has:

n = 9 + 18

n = 27

Which means, Liliana has 9 quarters and 27 nickels.

The probability that all fail on their first submissions is 27.1%.


For each student, there are only two possible outcomes. Either their first program run will fail, or it wont. The probability of the first program run of a student failing is independent of the first program run of other students. So we use the binomial probability distribution to solve this question.
Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.


In which  is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

The expected value of the binomial distribution is

The variance of the binomial distribution is

The standard deviation of the binomial distribution is

In this question, we have that:

83% of all students taking a beginning programming course fail to get their first program to run on first submission. Sample of 7 students. This means that

All fail on their first submissions

So,

0.271 = 27.1% probability that all ail on their first submissions

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