Which set of numbers is closed under subtraction? *
Natural numbers
Integers
Irrational numbers
Odd numbers

Using a system of equations, the rental cost for a movie and a video game is as follows:

A system of equations is two or more equations solved concurrently or at the same time.

A system of equations is also described as simultaneous equations.

                                  Movies   Video     Total

                                                Games    Cost

First month rental           3          5          $32

Second month rental    12          2          $29

Let the rental cost per movie = x

Let the rental cost per video game = y

3x + 5y = 32 ... Equation 1

12x + 2y = 29 ... Equation 2

Multiply Equation 1 by 4:

12x + 20y = 128 ... Equation 3

Subtract Equation 2 from Equation 3:

12x + 20y = 128

-

12x + 2y = 29

18y = 99

y = 5.5

Substitute y = 5.5 in Equation 1 or 2:

12x + 2y = 29

12x + 2(5.5) = 29

12x + 11 = 29

12x = 18

x = 1.5

Thus, based on simultaneous equations, the rental cost for a movie is $1.50 while a video game's is $5.50.

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The relationship between the two variables is y=4/3 x+3.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

The coordinate points are (0, 3) and (3, 7)

Here, slope (m) = (7-3)/(3-0)

= 4/3

Substitute m=4/3 and (x, y)=(0, 3) in y=mx+c, we get

3=4/3(0)+c

c=3

So, the equation is y=4/3 x+3

Therefore, the relationship between the two variables is y=4/3 x+3.

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Answer and Step-by-step explanation:

Solution: given:

(a)

Mean = λ = µ = 2permm3

By using formula:

P(x = k) =  λk e- λ  / k!

P ( not A) = 1 – p(A)

Passion probability at k = 0

P( x = 0) = 20 e-2/ 0!

               = 0.1353

Probability of at least one inclusion:

P(x≥1) = 1- p(x=0) = 1 – 0.1353

            = 0.864

(b) Probability of at least 3 inclusions in 4.0 cubic millimeters.

Mean = λ = µ = 2 per mm3

Inclusion in 4 cubic mm = 4 x 2 per 4 mm3 = 8 per 4 mm3

P(not A) = 1 – p(A)

Passion probability at k = 0,1,2

P(x=0) = 80 e-8 / 0!

        = 0.00034

P(x = 1) = 81 e-8 / 1!

            = 0.00272

P(x = 2) = 82 e-8 / 2!

              = 0.01088

Probability at least 3 inclusion:

P(x≥3) = 1 – p(x<3) = 1 – p(x = 0) – p(x =1) – p(x = 2)

            = 1 – 0.00034 – 0.00272 – 0.01088

          = 0.98606

(c) . Volume of material to inspect such that the probability of at least one inclusion is 0.98

The probability of x ≥ 1 has to be equal to 0.98

P(x ≥ 1) = 0.98

P(x = 0) = p(x < 1)

            = 1 – p(x≥ 1) = 1 – 0.98

            = 0.02

Poission probability at k = 0

P(x = 0) = (2 n )0 e-2n / 0! = e-2n

e-2n = 0.02

taking ln on both sides :

-2 n = ln e-2n = ln 0.02

Divided by -2,

n = ln 0.02 / -2

    = 1.955

Volume is 1.955 mm3.

(d) Determine the mean inclusion per cubic millimeter such that the probability of at least one inclusion is 0.98.

The probability of x ≥ 1has to be at least 0.98

P(x ≥ 1 )≥ 0.98

P(x = 0 ) = p(x < 1 ) = 1 – p(x≥1) =  1- 0.98

           = 0.02

Poisson probability at k = 0

P(x = 0) = λ0 e-λ / 0! = e-λ

e-λ ≤ 0.02

taking ln on both sides:

ln e-λ ≤ ln 0.02

λ = ln 0.02 / -1

    = 3.912

Answer: 34,650 permutations

Answer: x = 12

Step-by-step explanation:

You're on the right track! You're right in saying that each angle has to be 60 degrees since they're supposed to add up to 180. However, the question is asking what x equals, so we set up the equation:

5x = 60

x = 12

Answer: yes, 1/3, 1/3x

Step-by-step explanation:

Does x vary directly with y?

This basically means is this a linear function and the answer is yes it is.

What is the constant of variation?

The constant of variation is 1/3 because you have to multiply each x value by 1/3 to get the y value

What is the function rule?

y = 1/3x

Answer:

Option D) 5

Step-by-step explanation:

In the given graph of a parabola, and the equation in vertex form, y = (x - k )²: The variable k represents the x-coordinate of the vertex, and the point where the axis of symmetry lies on the graph.  In the given graph, the vertex is the minimum point, occurring at point (5, 0). The x-coordinate of the vertex is also the value of k = 5.

Therefore, the correct answer is Option D) k = 5.

The total surface area of the solid shape made from the cube and cylinder is approximately 583.31 cm².

The side length of the cube is 8.7 cm, so the surface area of one face is A = 8.7²

= 75.69 cm²

Since there are six faces, the total surface area of the cube is 6 * 75.69 = 454.14 cm²

Since there are two circular bases, the total surface area of the bases is 2 * 22.91 = 45.82 cm².

In this case, the radius of the cylinder is 2.7 cm and the height is 4.9 cm, so the curved surface area is A_curved = 2 * π * 2.7 * 4.9 ≈ 83.35 cm².

Total surface area = surface area of the cube + surface area of the cylinder

Total surface area = 454.14 cm² + 45.82 cm² + 83.35 cm²

Total surface area ≈ 583.31 cm²

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:I need the same answer lol

Answer:

Step-by-step explanation:

Answer:

-3  im pretty sure

Step-by-step explanation:

function f's y-intercept is 4

function g's y-intercept is 1

4-1=3

f has to go down so it will be -3

Answer:

The answer is B

Step-by-step explanation:

Class A: mean is 4.8

Class B: mean is 4

Based on the distance that Jill is above sea level, and the distance of the whale, the difference in elevation is 1.35 km.

Jill's elevation relative to sea level is:

= +5/4 km

The whale's elevation relative to sea level is:

= - 0.1 km

The difference is therefore:

= 5/4 - (-0.1)

= 1.25 + 0.1

= 1.35 km

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Answer:

A, C

Step-by-step explanation:

Quadratic formula:

\(x = \frac{ - b± \sqrt{b^{2} - 4ac } }{2a} \)

a is the coefficient of x², b is the coefficient of x and c is the constant when a second degree polynomial is equal to zero. (ax² +bx +c= 0)

x² +5x +11= 0

a= 1, b= 5, c=11

Thus, using the quadratic formula:

\(x = \frac{ - 5± \sqrt{ {5}^{2} - 4(1)(11)} }{2(1)} \\ x = \frac{ - 5± \sqrt{25 - 44} }{2} \\ x = \frac{ - 5± \sqrt{ - 19} }{2} \)

∴The answers are A and C.

Answer:

Brayden split cups 8 3/10 of flour into batches of 2 1/2 cups. How many batches of flour did Brayden have?

Sophie has fabric cut into 2 1/2 pieces yards in length. If the original fabric was 8 3/10 yards, how long was each piece?

Step-by-step explanation:

Write both complex numbers in polar form: (exp(x) is the same as e ˣ)

z = 16 (cos(47°) + i sin(47°)) = 16 exp(i 47°)

w = 4 (cos(12°) + i sin(12°)) = 4 exp(i 12°)

→   zw = 64 exp(i (47° + 12°)) = 64 exp(i 59°)

→   zw = 64 (cos(59°) + i sin(59°))

Using the z-distribution, as we have the standard deviation for the population, the margin of error is given by:

b. 0.39.

The confidence interval is:

\(\overline{x} \pm z\frac{\sigma}{\sqrt{n}}\)

In which:

The margin of error is given by:

\(M = z\frac{\sigma}{\sqrt{n}}\)

In this problem, we have a 95% confidence level, hence\(\alpha = 0.95\), z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

As for the other parameters, we have that \(\sigma = 1.8, n = 81\).

Hence, the margin of error is given by:

\(M = z\frac{\sigma}{\sqrt{n}}\)

\(M = 1.96\frac{1.8}{\sqrt{81}}\)

\(M = 0.39\)

Hence option b is correct.

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The percentage error of the reading is 5.78%

Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words, the percent error is the relative error multiplied by 100.

Percent errors indicate how big our errors are when we measure something in an analysis process. Smaller percent errors indicate that we are close to the accepted or original value.

The formula is given as

Percentage error = [(Estimated value - Actual value) / Actual Value] * 100

Percentage error = [(100.5 - 95) / 95] * 100

Percentage error = 0.0578 * 100

percentage error = 5.78%

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Cindy measured and recorded the temperature of a liquid for an experiment. She used a poorly calibrated thermometer and noted the temperature as 100.5 degrees Fahrenheit. The actual temperature of the liquid was 95 degrees Fahrenheit. What was her percent error?

The highest height for the daily rainfall were for 5 and 6 inches

Dot plots are used to present data in the form of points or small circles. It is similar to a simplified histogram or bar graph in that the height of the bar made up of points represents the numerical value of each variable. Dot plots are used to represent small amounts of data.

From the given dot plot, we see the number of times for each height of rainfall.

Thus, we see that the highest number of times of rainfall height was from that of 5 and 6 inches.

Thus, we conclude those were the highest heights for the daily rainfall.

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The northerly component of the wind blowing at 15 m/s from the South East is approximately 10.605 m/s.

To determine the northerly component of a wind blowing from the South East, we need to consider the direction from which the wind is coming and its magnitude.

A wind blowing from the South East means it is coming from the South East direction towards the opposite direction, which is the North West. Since the wind is coming from the South East, we can say it has a southeasterly direction.

To find the northerly component, we need to break down the wind vector into its north and east components. The northerly component represents the part of the wind that is directed towards the north.

If we assume that the wind is blowing at an angle of 45 degrees with respect to the North, we can use trigonometry to find the components. Since the wind is blowing at 15 m/s, we can consider it as the hypotenuse of a right triangle.

The northerly component can be found using the sine of the angle:

Northerly Component = Wind Speed * sin(Angle)

Northerly Component = 15 m/s * sin(45°)

Using the value of sin(45°) (which is √2 / 2 ≈ 0.707), we can calculate the northerly component:

Northerly Component ≈ 15 m/s * 0.707

Northerly Component ≈ 10.605 m/s

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Answer:

The suspect possesses 0.4 ounces of cocaine.

Step-by-step explanation:

Mass Units Conversion

The mass can be expressed in several units like grams, kilograms, ounces, pounds, etc. Each unit can be converted to any other multiplying by a fixed number.

The international conventions state that 1 gr = 0.035274 ounces.

If a suspect is in possession of 10 grams of cocaine, its equivalent to ounces can be calculated as 10*0.035274=0.35 oz. Rounding to the nearest tenth it would be 0.4 oz.

Since 1/8 = 0.125 and 1/2 is 0.5, our subject should be charged as a Class C felony

Answer:

Given equations are,

5x+2y=−2        (1)

3x−5y=17.4      (2)

Multiply equation (1) by 5 and equation (2) by 2, we get,

5(5x+2y)=5×−2

∴25x+10y=−10          (3)

2(3x−5y)=2×17.4

∴6x−10y=34.8          (4)

Adding equations (3) and (4), we get,

31x=24.8

∴x=

31

24.8

​

Put this value in equation (1), we get,

5(

31

24.8

​

)+2y=−2

∴

31

124

​

+2y=−2

∴2y=−2−

31

124

​

∴2y=

31

−186

​

∴y=

31

−93

​

Step-by-step explanation:

Answer:

Option D,four is correct

Step-by-step explanation:

The tax withholding from the gross income of $951 is the gross income itself minus the income after tax withholding i.e $189  ($951-$762)

The percentage of the withholding =189/951=20% approximately

Going by the multiple  choices provided,option with 4,189 dollars seems to the correct option as that is the exact of the tax withholding on Robert's gross income and his earnings fall in between $950 and $960

The number of allowances that Robert has claimed is four. Option d is correct.

A withholding tax is a tax that an employer deducts from an employee's paycheck and delivers it straight to the government (federal income tax).

From the given information:

The tax allowance = Gross income - savings amount

The tax allowance = $951 - $762

The tax allowance = $189

From the weekly income between 950 and 960 data, we can see that the number of allowances claimed related to the withholding allowances are:

0  → $259

1   →  $242

2   → $224

3   → $207

4  → $189

5   → $173

6  →  $162

7   → $151

8  →  $140

Therefore, we can conclude that the number of allowances that Robert has claimed is four.

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We have proved that the Newton-Raphson iteration formula for solving the equation\(x^k e^x = 0\) is given by \(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n.\)

To prove that the Newton-Raphson method for solving the equation \(x^k e^x = 0\), where k is a constant, is given by the formula

\(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n,\)

we can start by considering the iterative process of the Newton-Raphson method.

Given an initial guess \(x_n\), we want to find a better approximation \(x_{n+1}\)that is closer to the root of the equation \(x^k e^x = 0.\)

The Newton-Raphson method involves the following steps:

Calculate the function value \(f(x_n) = x_n^k e^x_n\) and its derivative \(f'(x_n) = k x_n^(k-1) e^x_n.\)

Find the next approximation x_{n+1} by using the formula:

\(x_{n+1} = x_n - f(x_n) / f'(x_n)\)

Let's apply these steps to our equation \(x^k e^x = 0\):

Calculate the function value and its derivative:

\(f(x_n) = x_n^k e^x_n\\f'(x_n) = k x_n^(k-1) e^x_n\)

Find the next approximation x_{n+1} using the formula:

\(x_{n+1} = x_n - f(x_n) / f'(x_n)\)

Substituting the function value and its derivative:

\(x_{n+1} = x_n - (x_n^k e^x_n) / (k x_n^(k-1) e^x_n)\\= x_n - (x_n^k / k)\)

Simplifying the expression by combining like terms:

\(x_{n+1} = x_n - (x_n^k / k)\\= x_n - x_n^k / k\\= (k - 1) x_n + x_n^2 / k + x_n\)

Therefore, we have proved that the Newton-Raphson iteration formula for solving the equation\(x^k e^x = 0\) is given by \(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n.\)

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Answer:

mk?

Step-by-step explanation:

Reason:

The angles shown must add to 180 degrees if we want the top and bottom lines to be parallel. These angles are same side interior angles.

(x+4)+(3x) = 180

4x+4 = 180

4x = 180-4

4x = 176

x = 176/4

x = 44

Answer:

x=42because of 3x and f or g

Answer:

The blue box

Step-by-step explanation:

Youre talking about range which takes place on the y-axis (domain is the x-axis).

The top point is an open circle which indicates in the math world the parentheses and the bottom point 1 in a bracket as its a closed circle.

Answer:

Intersecting

Step-by-step explanation:

Answer:

it’s C, 5.2

hope i helped

ur wlcm :)

correct me if im wrong

Answer:

Choice A.

\(y = - {2}^{x} + 4\)

Step-by-step explanation:

Use graphing calculator

Answer:

Choice A.

Step-by-step explanation: