Use the drawing tools to form the correct answers on the graph.
Consider this linear function:

y=\frac{1}{2}x+1

Plot all ordered pairs for the values in the domain.

D: {-8, -4, 0, 2, 6}

Answer:

12 sure not sure not sure

=8/12

in reduced fraction= 2/3

its 2/3  

By the inclusion/exclusion principle,

\(P(A\cup B) = P(A) + P(B) - P(A\cap B)\)

\(P(A\cup B) = \dfrac23 + \dfrac45 - \dfrac35\)

\(P(A\cup B) = \dfrac{10}{15} + \dfrac{12}{15} - \dfrac9{15}\)

\(P(A\cup B) = \boxed{\dfrac{11}{15}}\)

Answer:

1/4

Step-by-step explanation:

It's going 1 up and 4 across

Answer:

I think that's the answer

To determine the optimal order size for tomato sauce for Mama Rosa, we need to use the economic order quantity (EOQ) formula. This formula is given as:

Economic Order Quantity (EOQ) = sqrt(2DS/H)

Where: D = Annual demand

S = Cost per order

H = Holding cost per unit per year

Since the EOQ is the optimal order size, Mama Rosa should order 4,648 quarts of tomato sauce each time she orders.  For Mama Rosa's tomato sauce ordering:

D = 360*120

= 43,200 Cost per order,

S = $50 Holding cost per unit per year,

H = 20% of

$1 = $0.20 Substituting the values in the EOQ formula,

we get: EOQ = sqrt(2*43,200*50/0.20)

= sqrt(21,600,000)

= 4,647.98 Since the EOQ is the optimal order size, Mama Rosa should order 4,648 quarts of tomato sauce each time she orders.  

LT = Lead time

V = Variability of demand during lead time Lead time is given as 5 days and variability of demand is the standard deviation, which is given as 50 quarts.

To determine the reorder point, we Using the z-score table, the z-score for a 2% service level is 2.05. Substituting the values in the safety stock formula. use the formula: Reorder point = (Average daily usage during lead time x Lead time) + Safety stock Average daily usage during lead time is the mean, which is given as 120 quarts. Substituting the values in the reorder point formula, we get: Reorder point = 622.9 quarts Therefore, Mama Rosa should order tomato sauce when her stock level reaches 622.9 quarts.

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The equation for the plane containing the line in the xy-plane where y = 2 and the line in the xz-plane where z = 3 is:

2x - 3z = 0

To find the equation of the plane, we need to determine the normal vector to the plane. The normal vector is orthogonal (perpendicular) to both the line in the xy-plane and the line in the xz-plane.

The line in the xy-plane where y = 2 can be represented as (x, 2, 0), where x is a parameter. Similarly, the line in the xz-plane where z = 3 can be represented as (x, 0, 3), where x is also a parameter.

To find the normal vector, we can take the cross product of the direction vectors of the two lines. The direction vector for the line in the xy-plane is (1, 0, 0), and the direction vector for the line in the xz-plane is (1, 0, 0). Taking the cross product, we get:

(1, 0, 0) × (1, 0, 0) = (0, 0, 0)

Since the cross product is zero, it means that the two direction vectors are parallel, and there is no unique normal vector. In this case, any vector perpendicular to both lines can serve as the normal vector.

We can choose the vector (2, 0, 3) as the normal vector. Using the point (0, 2, 3) on the plane, we can write the equation of the plane as:

2x - 3z + d = 0

Plugging in the coordinates of the point, we find that d = 0, so the equation of the plane is:

2x - 3z = 0

The equation of the plane containing the line in the xy-plane where y = 2 and the line in the xz-plane where z = 3 is 2x - 3z = 0. This equation represents a plane that is perpendicular to both the xy-plane and the xz-plane and passes through the point (0, 2, 3).

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Step-by-step explanation:

The product of two factors is positive if both factors have the same sign (both positive or both negative). So, we need to determine the intervals on the number line where the expression 5(x - 3)(x+3) is positive.

We can use a sign chart to determine the sign of the expression in each interval:

| interval | x - 3 | x + 3 | (x - 3)(x + 3) |

|--------------|---------|---------|-----------------|

| x < -3 | negative | negative | positive |

| -3 < x < 3 | negative | positive | negative |

| x > 3 | positive | positive | positive |

The expression is positive in the intervals where (x - 3)(x + 3) is positive, which are the intervals x < -3 and x > 3. Therefore, the solution to the inequality is:

x < -3 or x > 3

This means that x can be any value less than -3 or any value greater than 3. To express the solution set in interval notation, we can write:

(-∞, -3) U (3, ∞)

Therefore, the solution to the inequality 5(x - 3)(x+3) > 0 is (-∞, -3) U (3, ∞).

Answer:

The answer is 2

Step-by-step explanation: took the test and got it right

Answer: (x, y) = (10, 10)

Since x = y, replacing y with x in 6x - 3y = 30 we have 6x - 3x = 3x = 30, so x = 30/3 = 10. Then y = x = 10, so the solution is (10, 10).

i hope this helps! :D

Answer:

27.65

Step-by-step explanation:

C=πd=π·8.8≈27.64602

rounded to the nearest tenth would be 27.65

hoped this helped.

Answer:

No

Step-by-step explanation:

I believe at the point of (1,1)  there is a distinct sort of point where it looks like an edge or corner which means that it is not continuous.

Continuous means that there is no abrupt changes (google) and im sure you know this already (im just saying no offence to anyone's intelligence)

The given function is not continuous. The correct option is D.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

A continuous function in mathematics is one that causes the value of the function to continuously vary as the input changes over time. This indicates that there aren't any discontinuities or sudden changes in value.

The point of (1,1)  there is a distinct sort of point where it looks like an edge or corner which means that it is not continuous. Continuous means that there are no abrupt changes.

It is shown in the graph that the function is reducing continuously at the point ( 1,-1) and after that, there is a sudden change in the function after that it becomes constant or parallel to the x-axis.

Because there is a sudden change in the function it will be termed a discontinuous function.

Hence, the function is not continuous, and the correct option is D.

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Option D is correct, there are no extraneous solutions to the equation.

The given equation is \(\sqrt{8x+9} =x+2\)

Let us solve for x:

Take square root on both sides:

\(8x+9=(x+2)^2\)

\(8x+9=x^2+4+4x\)

Now take the variable terms and constants on one side:

\(x^2-4x-5=0\)

\(x^2-5x+1x-5=0\)

\(x(x-5)+1(x-5)=0\)

\((x+1)(x-5)=0\)

x=-1 and x=5 are solutions.

Now, we will check both solutions to find any extraneous solution as:

\(\sqrt{8x+9} =x+2\)

When x=-1

\(\sqrt{8(-1)+9} =-1+2\)

\(\sqrt{1}=1\) so, it is true.

Now check for x=5:

\(\sqrt{8(5)+9} =5+2\)

7=7

Hence, there is no extraneous solution to our given equation and option D is the correct choice.

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Complete question:

Solve the radical equation. square root of 8x+9=x+2

Which is an extraneous solution to the radical equation?

(a)x = −1

(b)x = 1

(c)x = 5

(d)There are no extraneous solutions to the equation.

To find a recursive Nevill's method when interpolating a table using a polynomial at x = 4.1, we can use the following steps:

Step 1: Set up the given data in a table with two columns, one for f(x) and the other for x.

f(x)             x

36               1.16164956

3.80201036       4.0

0.30663842       4.2

0.35916618       -123926000.4

Step 2: Begin by finding the first-order differences in the f(x) column. Subtract each successive value from the previous value.

Δf(x)            x

-32.19798964     1.16164956

-3.49537194      4.0

-0.05247276      4.2

Step 3: Repeat the process of finding differences until we reach a single value in the Δf(x) column. Continue subtracting each successive value from the previous one.

Δ^2f(x)          x

29.7026177       1.16164956

3.44289918       4.0

Step 4: Repeat Step 3 until we obtain a single value.

Δ^3f(x)          x

-26.25971852     1.16164956

Step 5: Calculate the divided differences using the values obtained in the previous steps.

Divided Differences:

Df(x)             x

36                1.16164956

-32.19798964     4.0

29.7026177       4.2

-26.25971852     -123926000.4

Step 6: Apply the recursive Nevill's method to find the interpolated value at x = 4.1 using the divided differences.

f(4.1) = 36 + (-32.19798964)(4.1 - 1.16164956) + (29.7026177)(4.1 - 1.16164956)(4.1 - 4.0) + (-26.25971852)(4.1 - 1.16164956)(4.1 - 4.0)(4.1 - 4.2)

Solving the above expression will give the interpolated value at x = 4.1.

Q2: To construct an approximation polynomial using the Hermite method, we follow these steps:

Step 1: Set up the given data in a table with three columns: f(x), f'(x), and x.

f(x)             f'(x)              x

2.572152         7.615964          1.2

3.602102         13.97514          1.3

5.797884         34.61546          1.4

14.101442        199.500           1.5

Step 2: Calculate the divided differences for the f(x) and f'(x) columns separately.

Divided Differences for f(x):

Df(x)            \(D^2\)f(x)           \(D^3\)f(x)

2.572152         0.51595           0.25838

Divided Differences for f'(x):

Df'(x)           \(D^2\)f'(x)

7.615964         2.852176

Step 3: Apply the Hermite interpolation formula to construct the approximation polynomial.

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Answer:

y = \(\frac{29}{3}\)

Step-by-step explanation:

88 = 10y + 30 - 4y , that is

88 = 6y + 30 ( subtract 30 from both sides )

58 = 6y ( divide both sides by 6 )

\(\frac{58}{6}\) = y , that is

y = \(\frac{29}{3}\)

Answer: Do 1.25(19,000.00) and you get 23,750

Step-by-step explanation:

Answer:70

Step-by-step explanation:

The following techniques are used to calculate depreciation expense:

                                                    2022          2023

A) Straight-line Method              $2,472        $2,472

B) Units Of Activity Method       $3,048        $2,448

C) Declining Balance method   $5,200        $4,160

Given that,

On January 12, 1202, Pronghorn Company spent $26,000 on a delivery truck. The vehicle is anticipated to be driven 103,000 miles throughout its anticipated 10-year useful life, with a salvage value of $1.280. Actual mileage of 12,700 in 2022 and 10,200 in 2023 was used to calculate depreciation costs.

A) Straight-line Method

B) Units Of Activity Method

C) Declining Balance method

We know that,

Let

Straight-line method = $2,472 annually ($24,720/10)

Units of activity method per mile = $0.24 ($24,720/103,000)

2022 = $3,048 (12,700 x $0.24)

2023 = $2,448 (10,200 x $0.24)

Declining-balance method rate = 20% (100/10 x 2)

2022 = $5,200 ($26,000 x 20%)

2-23 = $4,160 ($20,800 x 20%)

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Answer: He earned $40.

Step-by-step explanation: So at the begging he started with $12. When he washed cars, he  made some money off of that. At the end, he had $52. So now, you need to do 52-12, which equals 40. So, he earned $40 washing cars. Hope that helps.

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The required sample size is 566

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time.

Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. The confidence interval is used to find lower and upper values of unknown population parameter and is given by:

n = (Z² × p × (1-p)) / E²

Z=1.96 from standard normal distribution table

n = (1.96² × 0.38 × (1-0.38)) / 0.04²

n = 566

The required sample size is 566

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Answer:

  3 km/h

Step-by-step explanation:

You want to know the speed of the river current if floating 36 km downstream takes 9 h longer than the trip upstream in a boat with a speed relative to the current of 15 km/h.

The relation between time, speed, and distance is ...

  time = distance / speed

If c represents the speed of the current, then 15-c is the speed upstream. The relation between the travel times is ...

  36/(15 -c) = 36/c -9

Multiplying by c(15-c), we have ...

  36c = 36(15 -c) -9(c)(15-c) . . . . . . . multiply by c(15-c)

  36c = 540 -36c -135c +9c² . . . . . eliminate parentheses

  9c² -207c +540 = 0 . . . . . . . collect terms

  c² -23c +60 = 0 . . . . . . . . divide by 9

  (c -20)(c -3) = 0 . . . . values that make the factors zero are c=20, c=3

The speed of the current is 3 km/h.

__

Additional comment

The speed of the current cannot be greater than 15 km/h, or the boat could not go upstream. The speed of the current cannot be greater than 4 km/h, or the trip downstream would take less than 9 hours.

<95141404393>

The matrix has two distinct eigenvalues, λ1<λ2:

λ1=  0 has an algebraic multiplicity(AM)= 2 the dimension of the corresponding eigenspace (GM) is 1

λ2= 3 has an algebraic multiplicity(AM)= 1 the dimension of the corresponding eigenspace (GM) is 1

Matrix C is NOT diagonalizable.

The characteristic polynomial of the matrix C is given as p(λ) = -λ^2(λ-3). To find the eigenvalues, we set p(λ) = 0.

-λ^2(λ-3) = 0

This equation has two distinct eigenvalues, λ1 and λ2:

λ1 = 0, which has an algebraic multiplicity (AM) of 2 (since the exponent of λ^2 is 2). To find the dimension of the corresponding eigenspace (GM), we solve the system (C - λ1I)x = 0, which is already in the form of matrix C. Since there is only one independent vector, the GM for λ1 is 1.

λ2 = 3, which has an algebraic multiplicity (AM) of 1. To find the dimension of the corresponding eigenspace (GM), we solve the system (C - λ2I)x = 0. In this case, there is only one independent vector, so the GM for λ2 is also 1.

A matrix is diagonalizable if the sum of the dimensions of all eigenspaces (GM) equals the size of the matrix. In this case, the sum of GMs is 1 + 1 = 2, while the size of the matrix is 3x3. Therefore, the matrix C is not diagonalizable.

Your answer:
λ1 = 0, AM = 2, GM = 1
λ2 = 3, AM = 1, GM = 1
Matrix C is NOT diagonalizable.

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Answer:

x=42

y=12

Step-by-step explanation:

Answer:

The standard form of an equation depends on the type of function f(x) you are referring to. Here are some examples of standard forms for commonly used functions:

Linear function: f(x) = mx + b, where m is the slope of the line and b is the y-intercept.

Quadratic function: f(x) = ax^2 + bx + c, where a, b, and c are constants. This is also called the "vertex form" of the quadratic function.

Exponential function: f(x) = ab^x, where a and b are constants. This is also called the "base exponential form" of the function.

Logarithmic function: f(x) = loga(x), where a is the base of the logarithm.

There are many other types of functions, and each one has its own standard form.

Step-by-step explanation:

The margin of error of the given population proportion by applying an estimate of the standard deviation based on the simulation is equal to 0.06.

Sample proportion = 0.18

Number of trials = 100

Sample size = 50

To determine the margin of error for the population proportion using an estimate of the standard deviation,

we can use the range of the sample proportions from the simulation.

The margin of error is calculated as half of the range.

In this case, the minimum sample proportion is 0.28 and the maximum sample proportion is 0.40.

Range = Maximum sample proportion - Minimum sample proportion

Range = 0.40 - 0.28

           = 0.12

The margin of error is half of the range,

Margin of Error = Range / 2

Margin of Error = 0.12 / 2

                          = 0.06

Therefore, the margin of error of the population proportion, using an estimate of the standard deviation based on the simulation, is 0.06.

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The Confidence interval for the population proportion p is approximately 0.4832

To determine the lower bound of a two-sided 95% confidence interval for the population proportion p, we can use the formula for the confidence interval of a proportion.

The formula for the confidence interval of a proportion is given by:

CI = p ± zsqrt((p(1-p))/n)

where:

CI = confidence interval

p = sample proportion

z = z-score corresponding to the desired confidence level

n = sample size

Given:

Sample proportion (p) = 37/80 = 0.4625 (since 37 out of 80 bicycle wheels were found to have critical flaws)

Sample size (n) = 80

Desired confidence level = 95%

We need to find the z-score corresponding to a 95% confidence level. For a two-sided confidence interval, we divide the desired confidence level by 2 and find the z-score corresponding to that area in the standard normal distribution table.

For a 95% confidence level, the area in each tail is (1 - 0.95)/2 = 0.025. Using a standard normal distribution table or a z-score calculator, we can find that the z-score corresponding to an area of 0.025 is approximately -1.96.

Now we can plug in the values into the formula and solve for the lower bound of the confidence interval:

CI = 0.4625 ± (-1.96)sqrt((0.4625(1-0.4625))/80)

Calculating the expression inside the square root first:

(0.4625*(1-0.4625)) = 0.2497215625

Taking the square root of that:

sqrt(0.2497215625) ≈ 0.4997215107

Substituting back into the formula:

CI = 0.4625 ± (-1.96)*0.4997215107

Now we can calculate the lower bound of the confidence interval:

Lower bound = 0.4625 - (-1.96)*0.4997215107 ≈ 0.4625 + 0.979347415 ≈ 1.4418 (rounded to four decimal places)

Therefore, the lower bound of the two-sided 95% confidence interval for the population proportion p is approximately 0.4418 (rounded to four decimal places).

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Answer:

-4

Step-by-step explanation:

\((y^4-y^3-3) \times (2y^3-2)=...+[(-1)(-2)+(2)(-3)]y^3+...\\=...+[2-6]y^3+...\\=...+(-4)y^3+...\\\)

so coefficient of y^3=-4

Answer:

The second one. The -2y should have been +2y

Step-by-step explanation:

a negative multiplied by a negative gives you a positive

Answer:

it should be the second answer

Step-by-step explanation:

hope this helps

Answer:

3 4/9-1 1/2= 1 17/18

Step-by-step explanation:

Answer:

3 4/9-1 1/2= 1 17/18

Step-by-step explanation:

Answer:

y = 5/4 (x) + 7

Explanation:

Slope of a line (m): (y₂ - y₁) ÷ (x₂ - x₁)

       Slope: (2 - -3) ÷ (-4 - -8) = 5 ÷ 4 = 5/4

Point slope form: y - y₁ = m (x - x₁)

       Equation: y - 2 = 5/4 (x - -4)

                        distribute the 5/4

                        y - 2 = 5/4 (x) + 5

                        add 2 to both sides

                        y = 5/4 (x) + 7

I hope this helps!