What is the solution to this system of equations -3x+5y=-2
3x+7y=26

Answer:

45

Step-by-step explanation:

I took the test and got right

Answer:

11.8 % empty

Step-by-step explanation:

volume of cylinder : pi × r² × h

attention ! the question gives us diameter, so for radius we need to cut them in half.

Va = pi × (14/2)² × 9 = pi×49×9 = 1385.44236... ft³

Vb = pi × (10/2)² × 20 = pi×25×20 = 1570.79633... ft³

after filling B with everything in A there is still some empty volume in B

Vb empty = Vb - Va = 185.35397... ft³

so,

100% Vb = 1570.79633... ft³

1% Vb = 15.7079633... ft³

so, how often does 1% of the total volume of B fit into the remaining empty volume of B ?

185.35397... / 15.7079633... = 11.8%

a. The decimal is terminating and the rational number is 0.

b. The decimal is terminating and the rational number is 0.

c. The decimal is repeating and the rational number is 0.161616...

d. The decimal is terminating and the rational number is 0.

To write a rational number as a decimal, you need to divide the numerator by the denominator. Let's go through each option to determine which decimal is repeating or terminating.

a. 0: This decimal is terminating because there are no numbers after the decimal point. The rational number is 0.

b. 0: This decimal is also terminating because there are no numbers after the decimal point. The rational number is 0.

c. 0.16 overbar: This decimal has a line over the 16, indicating that it is repeating. The rational number is 0.161616...

d. 0: This decimal is terminating because there are no numbers after the decimal point. The rational number is 0.

So, to summarize:

a. The decimal is terminating and the rational number is 0.

b. The decimal is terminating and the rational number is 0.

c. The decimal is repeating and the rational number is 0.161616...

d. The decimal is terminating and the rational number is 0.

.

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Recall that a line A is perpendicular to a line B if they form a 90 degrees angle, as in the picture below:

Therefore, the only construction of the ones given that can be used to find a perpendicular line to AB is the second option.

Answer:

Y = √80 or 4√5

Step-by-step explanation:

According to the combined triangle, the green area would be 8. Since it is a right triangle, we can use the Pythagorean theorem: a² + b² = c²

in  this case, y would be the hypotenuse, or C in the equation.

thus, the equation would be:

 4² + 8² = C² where C is Y

 16 + 64 = C²

80 = C²

 √80 = √C²

C = √80 or 4√5

Y = √80 or 4√5

I hope this helped you!

Answer:

-1

Step-by-step explanation:

\(i^{26}\)

= \((i^{2} )^{13}\)

= \((-1)^{13}\)

= -1

The solutions to the given differential equations are:

To verify that each given function is a solution of the given differential equation, we will substitute the function into the differential equation and check if it satisfies the equation.

1. y' = 3x²; y = x³ + 7

Substituting y into the equation:

y' = 3(x³ + 7) = 3x³ + 21

The derivative of y is indeed equal to 3x², so y = x³ + 7 is a solution.

2. y' + 2y = 0; y = 3e^(-2x)

Substituting y into the equation:

y' + 2y = -6e^(-2x) + 2(3e^(-2x)) = -6e^(-2x) + 6e^(-2x) = 0

The equation is satisfied, so y = 3e^(-2x) is a solution.

3. y" + 4y = 0; y₁ = cos(2x), y₂ = sin(2x)

Taking the second derivative of y₁ and substituting into the equation:

y"₁ + 4y₁ = -4cos(2x) + 4cos(2x) = 0

The equation is satisfied for y₁.

Taking the second derivative of y₂ and substituting into the equation:

y"₂ + 4y₂ = -4sin(2x) - 4sin(2x) = -8sin(2x)

The equation is not satisfied for y₂, so y₂ = sin(2x) is not a solution.

4. y" = 9y; y₁ = e^(3x), y₂ = e^(-3x)

Taking the second derivative of y₁ and substituting into the equation:

y"₁ = 9e^(3x)

9e^(3x) = 9e^(3x)

The equation is satisfied for y₁.

Taking the second derivative of y₂ and substituting into the equation:

y"₂ = 9e^(-3x)

9e^(-3x) = 9e^(-3x)

The equation is satisfied for y₂.

5. y' = y + 2e^(-x); y = e^x - e^(-x)

Substituting y into the equation:

y' = e^x - e^(-x) + 2e^(-x) = e^x + e^(-x)

The equation is satisfied, so y = e^x - e^(-x) is a solution.

6. y" + 4y^2 + 4y = 0; y₁ = e^(-2x), y₂ = xe^(-2x)

Taking the second derivative of y₁ and substituting into the equation:

y"₁ + 4(y₁)^2 + 4y₁ = 4e^(-4x) + 4e^(-4x) + 4e^(-2x) = 8e^(-2x) + 4e^(-2x) = 12e^(-2x)

The equation is not satisfied for y₁, so y₁ = e^(-2x) is not a solution.

Taking the second derivative of y₂ and substituting into the equation:

y"₂ + 4(y₂)^2 + 4y₂ = 2e^(-2x) + 4(xe^(-2x))^2 + 4xe^(-2x) = 2e^(-2x) + 4x^2e^(-4x) + 4xe^(-2x)

The equation is not satisfied for y₂, so y₂ = xe^(-2x) is not a solution.

7. y" - 2y + 2y = 0; y₁ = e^x cos(x), y₂ = e^x sin(x)

Taking the second derivative of y₁ and substituting into the equation:

y"₁ - 2(y₁) + 2y₁ = e^x(-cos(x) - 2cos(x) + 2cos(x)) = 0

The equation is satisfied for y₁.

Taking the second derivative of y₂ and substituting into the equation:

y"₂ - 2(y₂) + 2y₂ = e^x(-sin(x) - 2sin(x) + 2sin(x)) = 0

The equation is satisfied for y₂.

8. y" + y = 3cos(2x); y₁ = cos(x) - cos(2x), y₂ = sin(x) - cos(2x)

Taking the second derivative of y₁ and substituting into the equation:

y"₁ + y₁ = -cos(x) + 2cos(2x) + cos(x) - cos(2x) = cos(x)

The equation is not satisfied for y₁, so y₁ = cos(x) - cos(2x) is not a solution.

Taking the second derivative of y₂ and substituting into the equation:

y"₂ + y₂ = -sin(x) + 2sin(2x) + sin(x) - cos(2x) = sin(x) + 2sin(2x) - cos(2x)

The equation is not satisfied for y₂, so y₂ = sin(x) - cos(2x) is not a solution.

9. y' + 2xy² = 0; y = 1 + x²

Substituting y into the equation:

y' + 2x(1 + x²) = 2x³ + 2x = 2x(x² + 1)

The equation is satisfied, so y = 1 + x² is a solution.

10 x²y" + xy' - y = ln(x); y₁ = x - ln(x), y₂ = -1 - ln(x)

Taking the second derivative of y₁ and substituting into the equation:

x²y"₁ + xy'₁ - y₁ = x²(0) + x(1) - (x - ln(x)) = x

The equation is satisfied for y₁.

Taking the second derivative of y₂ and substituting into the equation:

x²y"₂ + xy'₂ - y₂ = x²(0) + x(-1/x) - (-1 - ln(x)) = 1 + ln(x)

The equation is not satisfied for y₂, so y₂ = -1 - ln(x) is not a solution.

11. x²y" + 5xy' + 4y = 0; y₁ = x², y₂ = x^(-2)

Taking the second derivative of y₁ and substituting into the equation:

x²y"₁ + 5xy'₁ + 4y₁ = x²(0) + 5x(2x) + 4x² = 14x³

The equation is not satisfied for y₁, so y₁ = x² is not a solution.

Taking the second derivative of y₂ and substituting into the equation:

x²y"₂ + 5xy'₂ + 4y₂ = x²(4/x²) + 5x(-2/x³) + 4(x^(-2)) = 4 + (-10/x) + 4(x^(-2))

The equation is not satisfied for y₂, so y₂ = x^(-2) is not a solution.

12. x²y" - xy' + 2y = 0; y₁ = xcos(ln(x)), y₂ = xsin(ln(x))

Taking the second derivative of y₁ and substituting into the equation:

x²y"₁ - xy'₁ + 2y₁ = x²(0) - x(-sin(ln(x))/x) + 2xcos(ln(x)) = x(sin(ln(x)) + 2cos(ln(x)))

The equation is satisfied for y₁.

Taking the second derivative of y₂ and substituting into the equation:

x²y"₂ - xy'₂ + 2y₂ = x²(0) - x(cos(ln(x))/x) + 2xsin(ln(x)) = x(sin(ln(x)) + 2cos(ln(x)))

The equation is satisfied for y₂.

Therefore, the solutions to the given differential equations are:

y = x³ + 7

y = 3e^(-2x)

y₁ = cos(2x)

y₁ = e^(3x), y₂ = e^(-3x)

y = e^x - e^(-x)

y₁ = e^(-2x)

y₁ = e^x cos(x), y₂ = e^x sin(x)

y = 1 + x²

y₁ = xcos(ln(x)), y₂ = xsin(ln(x))

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The corresponding polar coordinates are (10, 2π/3). Option B

From the information given, we have;

(-5, 5√3)

Given that the polar coordinates are represented as;

r = √(x² + y²)

θ = arctan(y / x)

We get;

\(r = \sqrt{(-5)^2} + (\sqrt{5} /3)^2\)

Find the value of square, we have;

r = \(\sqrt{25 + 75}\)

Add the values, we get;

r = \(\sqrt{100}\)

Find the square root

r = 10

To determine the value of theta, we get;

θ = arctan((-5√3) / -5)

Divide the values, we have;

θ = arctan(√3)

θ = 60 degrees

Then, we have; (10, 2π/3)

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Answer:

9 1/10th m/s2 :)

Step-by-step explanation:

The reason it is 1/10 is because the Number is 81 not 80, therefore 1/10 because there it is 1 left in 80 making it a fraction not a whole :) i hope this helps sorry if the explanation is too complicated...

Answer:

a = 12

Step-by-step explanation:

Pythagoras’ Theorem

a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

From inspection of the triangle:

Substituting these values into the formula and solving for b:

⇒ a² + 9² = 15²

⇒ a² + 81 = 225

Subtract 81 from both sides:

⇒ a² + 81 - 81 = 225 - 81

⇒ a² = 144

Square root both sides:

⇒ √(a²) = √(144)

⇒ a = 12

\(\qquad\qquad\huge\underline{{\sf Answer}}\)

Let's calculate the value of a using Pythagoras theorem ~

\(\qquad \sf  \dashrightarrow \: c {}^{2} = a {}^{2} + {b}^{2} \)

\(\qquad \sf  \dashrightarrow \: a {}^{2} = {15}^{2} - {9}^{2} \)

\(\qquad \sf  \dashrightarrow \: a= \sqrt{225-81} \)

\(\qquad \sf  \dashrightarrow \: a= \sqrt{144} \)

\(\qquad \sf  \dashrightarrow \: a= 12\: units\)

The chi-square statistic is used to determine whether there are differences between two nominally scaled variables. Chi-Square is a statistical test used to compare two nominal variables to determine whether they differ.

The Chi-Square test is used to test for differences between two groups. When you want to compare groups or examine the relationship between two variables, this test is useful. The chi-square test is a method of statistical inference that can be used to compare observed frequencies with expected frequencies, allowing us to determine whether there is a meaningful difference between them. When the p-value obtained from a chi-square test is less than 0.05, it is generally considered statistically significant.

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1 - x - x² - x³ - x⁴ - x⁵ - x⁶ can be shown generating number of ways considering number of die rolls as infinite series and showing that expression is equivalent to the generating function.

To show that (1 - x - x² - x³ - x⁴ - x⁵ - x⁶)-¹ is the generating function for the number of ways a sum of r can occur if a die is rolled any number of times, we'll follow these steps:

1. Identify the generating function for a single die roll.
2. Consider the infinite series representing any number of die rolls.
3. Show that the given expression is equivalent to the generating function.

Step 1: For a single die roll, the possible outcomes are 1, 2, 3, 4, 5, and 6. The generating function representing this is:
F(x) = x + x²+ x³ + x⁴+ x⁵+ x⁶

Step 2: To consider any number of die rolls, we want to find the generating function that represents the sum of outcomes for an infinite number of rolls. This is the sum of the geometric series with a common ratio F(x), so the infinite series is:

G(x) = 1 + F(x) + F(x)² + F(x)³ + ...

Step 3: To show that the given expression is equivalent to the generating function, we want to show that G(x) = (1 - x - x² - x³- x⁴- x⁵ - x⁶)-¹.

We know that the sum of an infinite geometric series is:

Sum = 1 / (1 - r)

Here, r = F(x), so the sum of the series G(x) is:

G(x) = 1 / (1 - F(x))

Now, substitute F(x) from Step 1:

G(x) = 1 / (1 - (x + x²+ x³+ x⁴+ x⁵ + x⁶))

G(x) = 1 / (1 - x - x² - x³- x⁴- x⁵- x⁶)

Thus, we have shown that (1 - x - x²- x³ - x⁴ - x⁵ - x⁶)-¹ is the generating function for the number of ways a sum of r can occur if a die is rolled any number of times.

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Answer:

Step-by-step explanation:

X=-x^2+x-5

25x + 45y ≤ 1,200

25x representing how much Richie would get paid in total (x representing the hours), 45y representing how much Justin would get paid in total (y representing the hours), ≤ representing less than or equal to, 1,200 is the greatest amount that Kirk can pay.

Answer:

\( 6\sqrt{6} \)

Step-by-step explanation:

\( \sqrt{12}\sqrt{18} = \)

\( = \sqrt{12 \cdot 18} \)

\( = \sqrt{4 \cdot 3 \cdot 9 \cdot 2} \)

\( = \sqrt{36 \cdot 6} \)

\( = \sqrt{36}\sqrt{6} \)

\( = 6\sqrt{6} \)

Following are the step by step solutions to the given expression:

Given:

\(\to \sqrt{12} \times \sqrt{18} \sqrt{30}\)

To find:

solve=?

Solution:

\(\to \sqrt{12} \times \sqrt{18} \sqrt{30}\)

\(\to \sqrt{2\times 2 \times 3} \times \sqrt{2\times 3 \times 3} \sqrt{2 \times 3 \times 5} \\\\ \)

\(\to 2\sqrt{3} \times 3\sqrt{2} \sqrt{2 \times 3 \times 5} \\\\ \to 6\times \sqrt{3} \times \sqrt{2} \sqrt{2\times 3 \times 5} \\\\ \to 6\times \sqrt{3} \times \sqrt{2} \times \sqrt{2}\times \sqrt{3} \times \sqrt{5} \\\\ \to 6 \times 3 \times 2 \times \sqrt{5} \\\\ \to 36 \sqrt{5}\)

Therefore, the final answer is "\(36\sqrt{5}\)"

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\((7d+6)-(-3d-5) \\ \\ =7d+6+3d+5 \\ \\ =\boxed{10d+11}\)

The parameter of interest is the proportion of people in the original group who had not smoked over the past 6 months.

We can calculate the parameter of interest by taking the number of people in the sample who had not smoked over the past 6 months (210) and dividing it by the total number of people in the sample (1000). This gives us a proportion of 0.21, or 21%. This tells us that 21% of people in the original group had not smoked over the past 6 months. This proportion is the parameter of interest in this scenario.

210/1000 = 0.21 or 21%

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Answer: See below.

Step-by-step explanation:

See attachment. It depends on what is considered the "third" term. If n=2 then the result is 16. If 3, the result is 36.

Surface area of cuboid  is = 312 ,With dedication and effort, you can succeed in your geometry test and feel confident about your understanding of the subject.

Surface area of a cuboid is = 2lw + 2lh + 2 hw

where ; l= length

w= width.

h = height

= 2(10×6)+2(10×6)+2(6×6)

=2(60)+2(60)+2(36)

=120+120+72

=312

Geometry can be challenging, but with the right mindset and approach, you can do well. To start, make sure you understand the basic concepts and definitions.

Then, practice solving problems and applying those concepts. Don't be afraid to ask questions or seek help when you need it. Utilize resources such as textbooks, online tutorials, and practice worksheets.

Also, try to relate geometry to real-life situations to make it more interesting and relevant. Remember to take breaks and stay organized to avoid feeling overwhelmed.

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Answer:

  1/4

Step-by-step explanation:

You want the probability that a random choice from a menu of 9 items, including 3 vegetables, is a vegetable after one vegetable has already been chosen. The second choice is different from the first.

After choosing one vegetable, the available different items remaining on the menu are 2 vegetables among a total of 8 items.

The probability that the second random choice will be a vegetable is ...

  (2 vegetables)/(8 items) = 2/8 = 1/4

The probability that the second choice is also a vegetable is 1/4.

__

Additional comment

Since the choices must be different, the first choice is essentially removed from the menu. Since we're only concerned with the second choice, we don't need to consider the probability that the first choice was a vegetable.

Answer: 1/4

Step-by-step explanation: 1-3/4

Answer:  1 subtracted by 3/4 is -0.25  (Decimal form) but as a fraction, it's  -1/4. (Fraction form)

If this is not what you want or doesn't help. Just let me know and I'll see what I can do!

The given numerical value of $44,000 represents the average salary of all assembly-line employees at a certain car manufacturer. Hence, it is a parameter.

In statistical analysis, the terms "parameter" and "statistic" are used to distinguish between population characteristics and sample characteristics, respectively. To determine whether the given numerical value represents a parameter or a statistic, we need to understand the context in which the value is used.

A parameter refers to a numerical value that describes a characteristic of a population. It represents a fixed, unknown value and is typically denoted by Greek letters. Parameters are derived from data collected from an entire population.

On the other hand, a statistic refers to a numerical value that describes a characteristic of a sample. It is computed from a subset of data, known as a sample, and is used to estimate the corresponding population parameter.

In the given statement, the average salary of all assembly-line employees at a certain car manufacturer is stated to be $44,000. Since this value represents the average salary of all employees in the population, it is a parameter. The value is derived from information about the entire population of assembly-line employees at the car manufacturer, rather than a sample.

If the statement had mentioned the average salary of a sample of assembly-line employees, then the numerical value would have been a statistic. In that case, it would have been computed from a subset of the data (a sample) and used to estimate the average salary of the entire population.

In summary, the given numerical value of $44,000 represents the average salary of all assembly-line employees at a certain car manufacturer. Hence, it is a parameter.

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Answer:

178,303,038

Step-by-step explanation:

Multiply it

Or put it into a calculator

Answer:

an average weight of 10student was calculated to be 75. later it was discovered thatone weight wss insread as 35 instead of 50k.g. calculate the correct average weight

A ray has only one endpoint. A segment has two endpoints.

What is a line?

A line is an object in geometry that is infinitely long and has neither width nor depth nor curvature. Since lines can exist in two, three, or higher-dimensional spaces, they are one-dimensional objects. In everyday language, a line segment with two points designating its ends is also referred to as a "line."

A ray and a segment are parts of a line.

This line segment has two fixed-length endpoints, A and B. The distance between this line segment's endpoints A and B is its length.

In other words, a line segment is a section or element of a line with two endpoints. A line segment, in contrast to a line, has a known length.

A line segment's length can be calculated using either metric units like millimeters or centimeters or conventional units like feet or inches.

Ray has only one endpoint and the other ends go infinity.

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Polynomial equation is a equation which is formed with coefficients variables and exponents with basic mathematics operation and equality sign. From the given option the option C correctly combines the like terms and puts the given polynomial in standard form which is,

\(8x^4-\dfrac{2}{3}x^2-\dfrac{2x}{3}\\\)

Hence the option C is the correct option.

The given polynomial equation in the problem is,

\(\dfrac{1}{3} x+8x^4-\dfrac{2}{3}x^2-x\)

Polynomial equation is a equation which is formed with coefficients variables and exponents with basic mathematics operation and equality sign.

In the above polynomial equation the variable are x and the highest power of the variable x is four.

Arrange the given polynomial equation in the power of the variable x. Thus,

\(8x^4-\dfrac{2}{3}x^2+\dfrac{1}{3} x-x\)

Make the group of the same power of the variable x. Therefore,

\(8x^4-\dfrac{2}{3}x^2+(\dfrac{1}{3} x-x)\)

\(8x^4-\dfrac{2}{3}x^2+\dfrac{x-3x}{3}\\\)

\(8x^4-\dfrac{2}{3}x^2-\dfrac{2x}{3}\\\)

From the given option the option C correctly combines the like terms and puts the given polynomial in standard form which is,

\(8x^4-\dfrac{2}{3}x^2-\dfrac{2x}{3}\\\)

Hence the option C is the correct option.

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Answer:

See below.

Step-by-step explanation:

The answer is 4x+5y=6.

A linear function has a single slope. A function with exponents will not be linear.

-hope it helps

Given two predictor variables with a correlation of 0.32879, we should expect there to be multicollinearity between them.

In a data set with a, b, c, d, e, and f numeric variables, given there is a strong correlation of these pairs (f, a), (f, c), (d, e), (a, d), we can set up a regression model as

Of-a + c Of-a + b + c + d + e Of-a + C + d + e Of-a + C + e.

Given two predictor variables with a correlation of 0.32879, we should expect there is multicollinearity between them.

The statement that is true regarding the given two predictor variables with a correlation of 0.32879 is:

we should expect there to be multicollinearity between them.

Multicollinearity is a situation in which two or more predictor variables in a multiple regression model are highly correlated with one another. Multicollinearity complicates the understanding of which predictor variables are significant in the regression model's estimation.

Therefore, given two predictor variables with a correlation of 0.32879, we should expect there to be multicollinearity between them.

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Three segments a, b, and c using net sales as the basis for allocation is = $475,000.

Based on the given conditions,

Three segments are a , b , c

The segment a of trump enterprises have net sales = $300,000

The segment b of trump enterprises have net sales = $150,000

The segment c of trump enterprises have net sales = $50,000

a net sales + b net sales + c net sales = $300,000 + $150,000 + $50,000

= $500,000

If the unit is eliminated, then the a net sales and b net sales will be gone, but the c net sales will be allocated to other business units.

So instead of losing $500,000,

A decision is made to allocate the pool = $25,000

The company's net sales as the basis for allocation by $500,000 - $25,000 = $475,000

Therefore,

Three segments a, b, and c using net sales as the basis for allocation is =

$475,000.

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Answer: k = √27-i

Step-by-step explanation: