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Cramer's rule states that the solution to a system of equations can be determined by taking the determinant of the coefficient matrix, which in this case is 4, and then dividing each equation's determinant of the corresponding matrix by the determinant of the coefficient matrix. This allows us to solve for the variable y.

Cramer's Rule is a method used to solve systems of linear equations. It states that the solution to a system of equations can be determined by taking the determinant of the coefficient matrix and then dividing each equation's determinant of the corresponding matrix by the determinant of the coefficient matrix. This gives us the solution for the variable y. To calculate the determinant of the coefficient matrix, we take the product of the diagonal elements and subtract the product of the elements that are not on the diagonal The determinant is calculated by taking the product of a and d, and then subtracting the product of b and c. Once we have the determinant of the coefficient matrix, we can calculate the determinants of each equation's corresponding matrix by replacing the y in the equation with 1 and the other coefficients with the original coefficients of the equation. We then divide each equation's determinant by the determinant of the coefficient matrix to solve for y. This method is useful as it allows us to solve a system of equations with multiple variables in a quick and efficient manner.

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Answer:

Step-by-step explanation:

5x - 16 = 4x + 6

x - 16 = 6

x = 22

5(22) - 16 = 110 - 16 = 94

4(22) + 6 = 88 + 6 = 94

Answer:

520 out of 800 students ride the bus

Step-by-step explanation:

Given

\(Proportion = 65\%\)

\(Students = 800\)

Required

Determine the number of students \(that\ ride\ the\ bus\)

To do this, we simply multiply the proportion by the total number of students.

i.e.

\(Bus = Proportion * Students\)

\(Bus = 65\% * 800\)

Express the percentage as decimal

\(Bus = 0.65* 800\)

\(Bus = 520\)

Answer:

C: 52 degrees

Step-by-step explanation:

Answer:

The answer is 32

Step-by-step explanation:

The formula for finding the area of a trapezoid is:

         ((base 1 + base 2)/ 2 )* h

Now all you have to do is substitute the numbers in.

Note: bases will always be the ones like 12 and 4 in this case. We have just named then 1 and 2.

Answer:

32 square units

Step-by-step explanation:

\(\displaystyle A=\frac{1}{2}(b_1+b_2)h=\frac{1}{2}(12+4)(4)=\frac{1}{2}(16)(4)=\frac{1}{2}(64)=32\)

Note that \(b_1\) and \(b_2\) are the lengths of each base of the trapezoid, so it doesn't matter which is which.

Answer:

990.6

Step-by-step explanation:

61.8×17=9906 and since there is two number in the decimal point we put the decimal point in after the number 06

so it is......99.06

Using strategic thinking, the solutions to the following questions are:

Strategic thinking involves using rational thought processes to focus on workable solutions to business problems.

Strategic thinking concentrates on the future based on its changing environments.

In this situation, 50% of a number represents one-half of the given value.  We can divide each number by 2 to find the solutions.

a) 50% of 10 liters of milk = 5 liters (10 x 50%)

b) 50% of 2,000 kilometers = 1,000 kilometers (2,000 x 50%)

c) 50% of 24 hours = 12 hours (24 x 50%)

Thus, strategically thinking, half of each value represents its 50%.

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Ramiro has three credit cards with limits of $7,000, $5,000, and $9,500, respectively. Assuming he charged each of them up to 75 percent of its limit, the amount he owes on each card is:

Card 1: 75% of $7,000 = $5,250

Card 2: 75% of $5,000 = $3,750

Card 3: 75% of $9,500 = $7,125

To calculate the total amount Ramiro owes, we add up the amounts he owes on each card: $5,250 + $3,750 + $7,125 = $16,125

Therefore, Ramiro currently owes a total of $16,125 on his three credit cards.

By consideration of congruence and collinearity, the value of x behind the geometric system formed by two collinear linear segments is equal to 3 / 8.

Two line segments are congruent when the line segments have the same length, then the following condition has to be fulfilled:

AB = BC      (1)

Where AB and BC are the lengths of the line segments AB and BC.

If we know that AB = 4 · x + 1 and BC = 20 · x - 5, then we solve the equation for x is:

4 · x + 1 = 20 · x - 5

6 = 16 · x

16 · x = 6

x = 6 / 16

x = 3 / 8

Then, the value of x behind the geometric system formed by two collinear linear segments is equal to 3 / 8.

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Answer:

false and then true

Step-by-step explanation:

Hope this helps :)

Answer:

First one is False, second one is true.

Step-by-step explanation:

For the first one, the left side of the equation would equal -6/3, and the left side would be 3/-6. When simplified it would be: -2 = -1/2, which is incorrect.

For the second one, the left side and the right side are the same because either way you put it, they are still being multiplied, and the order doesn't matter. The end result will be -72 = -72, which is correct.

I hope this helps!! :>

Answer:

170, 171, 172

Step-by-step explanation:

x + x + 1 + x + 2 = 513

3x + 3 = 513

3x = 510

x = 170

x + 1 = 171

x + 2 = 172

The step that Inga could use to solve the quadratic equation is;

2(x² + 6x + 9) = 18 + 3.

The solution to the quadratic equation is calculated as follows;

2x² + 12x - 3 = 0

Add 3 to both sides to get;

2x² + 12x = 3

Divide through by 2 which is the coefficient of x² to get;

x² + 6x = ³/₂

Square half of the coefficient of x, and then add it both sides of the equation to get;

(x + 3)² = ³/₂ + 3²

x² + 6x + 9 = 9 + ³/₂

2(x² + 6x + 9) = 18 + 3

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The independent variable in this data is the speed of the car. This is because the congressman is trying to determine whether or not the gas mileage improves at lower speeds.

The dependent variable is the gas mileage, because it is the variable that is being measured and that is affected by the independent variable.

The other variables in this data are the weight of the car, the type of engine, and the year of the car. However, these variables are not being changed in this experiment, so they are not considered to be independent variables.

The data shows that the gas mileage of the Toyota Camry improves as the speed of the car decreases. This supports the claim of the supporters of the bill to reduce the speed limit.

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Answer:

Step-by-step explanation:

The per capita emissions for each country is:

Using this formula to find the  Per capita emissions for each country

Per capita emissions = C02 Emission (tons of carbon dioxide ) /  Total emissions by population

China

Per capita emissions =8,782,000,000/1,359,750,000

Per capita emissions = 6.46

United States

Per capita emissions =5,144,000,000/316,597,000

Per capita emissions= 16.25

India

Per capita emissions = 2,185,000,000 /1,233,460,000

Per capita emissions = 1.77

Russia

Per capita emissions=1,646,000,000/143,400,000

Per capita emissions = 11.48

Japan

Per capita emissions = 1,232,000,000/127,310,000

Per capita emissions = 9.68

Germany

Per capita emissions = 733,000,000/80,523,700

Per capita emissions = 9.10

Iran

Per capita emissions = 583,000,000/76,876,000

Per capita emissions = 7.58

South Korea

Per capita emissions = 576,000,000/50,219,669

Per capita emissions = 11.47

Indonesia

Per capita emissions = 535,000,000/237,641,326

Per capita emissions = 2.25

Canada

Per capita emissions = 528,000,000/35,141,542

Per capita emissions =15.02

Therefore China per capita emissions is 6.46.

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Answer:

The number of passcodes possible is 1,100,000

Step-by-step explanation:

Here , we want to calculate the number of different possible passcodes.

For the five digit code,

each number in the code has a possibility of choosing from the digits 0 to 9, so this means that each of the numbers in the code has 10 options.

So for a five digit code, the number of possible choices would be 10 * 10 * 10 * 10 * 10 = 10^5

For a six digit code, the number of possible choice would be 10 * 10 * 10 * 10 * 10 * 10 * 10 = 10^6

So for 5 or 6 digits code, the number of possible choices would be;

10^5 + 10^6 = 10^5(1 + 10)

= 11(10^5) = 1,100,000

The number of passcodes possible is 1,100,000

For the five-digit code, the no of possible choices should be \(10^5\)

For the six-digit code, the no of possible choices should be \(10^6\)

So, the possible choices should be

\(10^5 + 10^6 = 10^5(1 + 10)\\\\= 11(10^5)\)

= 1,100,000

Hence, The number of passcodes possible is 1,100,000

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Answer:

3n + 5 = 23,

3n = 18

n = 6

since "n" = 6,

2n - 3

= 2×6 - 3

12 - 3

= 9

Well technically 24% cannot be a whole number

Step-by-step explanation:

first place 24% as a fraction = 24/100

Change it to it's lowest term = 6/25

And this can only be changed to a decimal= 0.24

Answer:

1000 tiles

Step-by-step explanation:

Determine total floor space
800 x 10 = 8000 squared cm total floor space.
Divide floor space by size of tile
8000 / 8 = 1000 tiles now required to cover the floor.

Step-by-step explanation:

red feeder is smarter

Complete question :

A study was designed to test whether applying metal tags is detrimental to a penguin. One variable examined is the survival rate 10 years after tagging. The scientists observed that 10 of the 50 metal tagged penguins survived, compared to 18 of the 50 electronic tagged penguins. Construct a 90% confidence interval for the difference in proportion surviving between the metal and electronic tagged penguins (). Let be the proportion of penguins with metal tags that survived and be the proportion of penguins with electronic tags that survived. Round your answers to three decimal places.

Answer:

(-0.305 ; - 0.015)

Step-by-step explanation:

Sample size, n1 = 50

x1 = 10

n2 = 50

x2 = 18

P1 = x1 / n1 = 10/50 = 0.2

P2 = x2 / n2 = 18 /50 = 0.36

1 - P1 = 0.8 ; 1 - P2 = 0.64

Zcritical at 90% = 1.645

Confidence interval :

(P1 - P2) ± Zcritical * standard error

Standard Error = sqrt[(p1(1-p1))/n1 + (p2(1-p2))/n2]

S.E = sqrt((0.2(0.8))/50 + 0.36(0.64))/50)

S.E = sqrt((0.0032 + 0.004608))

S. E = sqrt(0.007808)

S. E = 0.0883628

(0.2 - 0.36) ± (1.645 * 0.0883628)

-0.16 ± 0.145356806

Lower boundary = - 0.16 - 0.145356806 = −0.305356806

Upper boundary = - 0.16 + 0.145356806 = −0.014643194

(-0.305 ; - 0.015)

Answer:

X=6

Step-by-step explanation:

3 times 6 is 18 so x is 18

Answer:

\( \huge{ \fbox{ \sf{x = 6}}}\)

Step-by-step explanation:

\( \star{ \sf \: \: 3x = 18}\)

\( \text{ Step \: 1 \: : divide \: both \: sides \: by \: 3}\)

\( \mapsto{ \sf{ \frac{3x}{3} = \frac{18}{3} }}\)

\( \text{Step \: 2 : calculate}\)

\( \mapsto{ \sf{ x = 6}}\)

Hope I helped!

Best regards! :D

~\( \text{theanimegirl}\)

Answer:

9.76

Step-by-step explanation:

To complete the table it is necessary to know the possibilities that the sergeant has to change or remain in an intersection. The probabilities (depending on the box) are:

To know the probability of intersection change, it is necessary to locate the police officer at one of the intersections. Subsequently, count how many possibilities of change you have, for example: 3 possibilities and finally add the possibility of remaining in the intersection as shown below:

To know the probability we divide the number 1 (because it is only a decision that we have to make) and divide it by the number of possibilities (4).

According to the image we can infer that in some intersections they only have 3, 4 and 5 possibilities, so the probability of change will be different as shown below:

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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 meaning of the statement, "if the function has no parameters, then the class C is definable" is that if there are no parameters given then the class c can be defined with an empty set but if there are no parameters, then the class cannot be defined.

The meaning of the above statement is that if no parameters are provided for this function, then the given class represented as c can be defined with an empty set that is enclosed in parameters.

Also, if the parameters are given then the class c is not defined.

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Answer:

Not A

Not B

Not C

D is the answer.

Step-by-step explanation:

Answer:

the answer is p = 15

Step-by-step explanation:

first you set the equation to 2p + 9 = 3p - 6

then solve out the equation by adding 6 to both sides

the equation will now look like this, 2p + 15 = 3p

now you subtract 2p from both sides

the equation now looks like 15 = p

I always flip my equations so I can read it better,

p = 15

Hope this helps! :)

Answer:

The price of the shirt is $24.63.

Step-by-step explanation:

Let's assume the price of the shirt is x. Then the price of the wallet will be x - 15. We know that the total cost before tax is 34.26, so we can set up the equation:

x + (x - 15) = 34.26

Simplifying, we get:

2x - 15 = 34.26

Adding 15 on both sides:

2x = 49.26

Dividing by 2:

x = 24.63

Therefore, the price of the shirt is $24.63.