find f g, f − g, fg, and f/g and their domains. f(x) = x, g(x) = 9x

Answer:it’s “c”

Step-by-step explanation:

First you’re going to get the slope (15+3)/(6-0)=3 —- 15+3 because you have two negatives which makes the sign positive

And you already have a bracket (0,-3)

If x in the bracket is 0 then the y is the y intercept

The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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The factor (x - 1) exists. Therefore, the polynomial must be equal to zero for x = 1. f(1) = 0 is true as a result.

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Given

csc(-420)

Find

Value of given function

Explanation

Final Answer

40 m³ is the volume of pyramid .

What is a pyramid defined as?

A three-dimensional shape is a pyramid. A pyramid's flat triangular faces and polygonal base all come together in a summit known as the apex. By fusing the bases together at the peak, a pyramid is created. The lateral face, a triangular feature formed by the connection of each base edge to the apex, is present.

  L= 5

h = 4

s = 6

V = 6 * 4 * 5/3

   = 120/3

   = 40 m³

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Given the question we conclude that Harmony's total monthly salary, including commission, would be $1,967.75.

Harmony's base monthly salary is $850. In addition to her salary, she earns a commission of 12.5% on everything she sells. This month, Harmony sold $9,826 worth of products. To calculate her commission, we multiply the sales amount by the commission rate:

Commission = $9,826 × 12.5% = $1,228.25

To find her total monthly salary, we add her base salary and the commission:

Total Monthly Salary = Base Salary + Commission

                    = $850 + $1,228.25

                    = $2,078.25

Therefore, Harmony's total monthly salary, including commission, would be $2,078.25. However, it's important to note that this exceeds her base salary of $850. Since the question asks for her total monthly salary, we need to subtract her base salary from the calculated total:

Total Monthly Salary = $2,078.25 - $850

                                  = $1,228.25

Therefore, Harmony's total monthly salary, including commission, would be $1,228.25.

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The perimeter of the triangle will be 8.064.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The vertices of the triangle are,

A = (2, 1)

B = (5, 1)

C = (4, 3)

Now,

We find the distance between the vertices of the triangle which is equal to the length of the side.

So, Distance between the points A (2, 1) and B (5, 1) is calculated as;

Length of AB = √(5 - 2)² + (1 - 1)²

                     = √3²

                     = 3

Length of BC = √(4 - 5)² + (3 - 1)²

                    = √1 + 4

                    = √5

                    = 2.236

The length of CA = √(2 - 4)² + (1 - 3)²

                          = √4 + 4

                          = √8

                          = 2.828

Thus, Perimeter of triangle = Length of AB + Length of BC + Length of CA

Substitute all the value we get;

Perimeter of triangle = 3 + 2.236 + 2.828

                                = 8.064

Therefore, The perimeter of the triangle will be 8.064.

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\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{60\% of 15}}{\left( \cfrac{60}{100} \right)15}\implies 9~\hspace{7em} \stackrel{15-9}{6}\)

Answer:

-9

Step-by-step explanation:

Answer:

a and d

Step-by-step explanation:

Answer: 491 cards

Step-by-step explanation:

Given

Steve had 10 more cards than Jeff

Suppose Jeff has x cards

So, steve has x+10 cards

Steve handover his cards to Jeff

Now, Jeff has x+x+10=2x+10 cards

It must be equal to 992

\(\Rightarrow 2x+10=992\\\Rightarrow 2x=982\\\Rightarrow x=491\ \text{cards}\)

Jeff started with 491 cards

Ground-state electron configuration of gas-phase Co²+ is [Ar] 3d⁷. Answer: (E) [Ar] 3d⁷.Explanation: First of all, we need to find the electron configuration of Cobalt (Co).

The electron configuration of Cobalt (Co) is 1s²2s²2p⁶3s²3p⁶4s²3d⁷.Now, we can remove the electrons to get the electron configuration of gas-phase Co²+ .Co: 1s²2s²2p⁶3s²3p⁶4s²3d⁷Co²+: 1s²2s²2p⁶3s²3p⁶3d⁷The full electron configuration of Co²+ will be [Ar] 3d⁷. Therefore, the answer is (E) [Ar] 3d⁷.

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Answer:

4 km -> 400,000 mm

put a decimal point at the end of 4 and move it to the left 6 times because we know that 1 km is equal to 100,000 and it has zeros.

hence, it is proven that 4 km is equal to 4000,000.

a) To calculate the difference between the before and after measurements, we subtract the after measurements from the before measurements:

Person 1: 81 - 73 = 8

Person 2: 84 - 77 = 7

Person 3: 79 - 73 = 6

Person 4: 85 - 78 = 7

Person 5: 79 - 71 = 8

Person 6: 84 - 75 = 9

Person 7: 87 - 80 = 7

These values represent the differences in heart rate before and after exercise for each person.

(b) To construct a 95% confidence interval for the mean reduction in heart rate, we can use the TInterval function on a calculator or statistical software. Given that the sample size is small (n = 7), it is appropriate to use a t-distribution for the confidence interval.

Using the provided data, enter the differences calculated in part (a) into L1 on the calculator. Then, follow these steps to obtain the confidence interval:

Select the TInterval function on your calculator or statistical software.

Choose a confidence level of 95%.

Enter the list containing the differences (L1) as the data set.

Calculate the confidence interval.

The calculator or software will provide you with the 95% confidence interval for the mean reduction in heart rate, rounded to two decimal places.

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Answer:

the first half of the play is 95 minutes long

Step-by-step explanation:

155-35= 120 (you subtract 35 so you get the number if both plays lasted the same time )

120/2= 60 (you get the amount of time one play lasted without extra 35 minutes)

60+35=95 (then add 35 minutes to one play because 1 one is longer than the other one)

the first half of the play is 95 minutes long.

The average number of beads that the girls have is 63

Let's start by using algebra to represent the given information:

Let b be the number of beads that Sally has.

Then, Kelly has 3/4 times as many beads as Sally, which can be expressed as (3/4)b.

Also, we know that Kelly has 18 more beads than Sally, which can be expressed as (b + 18).

Putting these together, we can write the equation:

(3/4)b = b + 18

Solving for b, we get:

b = 72

So, Sally has 72 beads, and Kelly has (3/4) × 72 = 54 beads.

The average number of beads that the girls have is (72 + 54)/2 = 63 beads

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Answer:

The equation of the circle is (x - 2)^2 + (y - 5)^2 = 100.

Before the launching its latest line of health drinks, a beverage manufacturer provided free samples of the health drinks to a large and culturally diverse set of families. This is a qualitative research.

Qualitative research is the study of the nature of phenomena and is particularly effective for clarifying why something is (or is not) seen, assessing complicated multi-component interventions, and focusing on intervention improvement.

Data from first-hand observation, interviews, questionnaires, focus groups, participant-observation, recordings recorded in natural settings, documents, case studies, and artifacts are used in qualitative research. The information is mostly non-numerical.

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Answer:

P(x) = 35,900 + 2,800(x-1)

Step-by-step explanation:

P(x)

P(1) = $35,900

P(4) = $44,300

Difference in profits

P(4) - P(1)

= P(3)

= $44,300 - $35,900

= $8,400

Rate of change per year = $8,400 / 3

= $2,800 per year

The linear equation

P(x) = 35,900 + 2,800(x-1)

Where

x = number of years

Danny used half a cup of flour, so Paul Bunyan would need  2 cups of flour for his foot-diameter griddle.

To determine the number of cups of flour Paul Bunyan would need for his circular griddle, we need to compare the surface areas of the two griddles.

We know that Danny Henry's griddle has a diameter of six inches, which means its radius is three inches (since the radius is half the diameter). Thus, the surface area of Danny's griddle can be calculated using the formula for the area of a circle: A = πr², where A represents the area and r represents the radius. In this case, A = π(3²) = 9π square inches.

Now, let's calculate the radius of Paul Bunyan's griddle. We're given that it has a diameter in feet, so if we convert the diameter to inches (since we're using inches as the unit for the smaller griddle), we can determine the radius. Since there are 12 inches in a foot, a foot-diameter griddle would have a radius of six inches.

Using the same formula, the surface area of Paul Bunyan's griddle is A = π(6²) = 36π square inches.

To find the ratio between the surface areas of the two griddles, we divide the surface area of Paul Bunyan's griddle by the surface area of Danny Henry's griddle: (36π square inches) / (9π square inches) = 4.

Since the amount of flour required is directly proportional to the surface area of the griddle, Paul Bunyan would need four times the amount of flour Danny Henry used.

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The probability that the next person will pay with a debit card is:

P =  0.63

We want to find he probability that the next customer will pay with a debit card.

That probability can be estimated as the quotient between the number of customers that paid with debit card and the total number of customers.

We know that:

15 paid in cash.

50 paid with debit card.

15 paid with credit card.

For a total of 15 + 50 + 15 = 80

Then the probability is:

P = 50/80 = 0.63

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The value of the integral (9x + 9y) da over the region r is approximately 14.0625.

To evaluate the given integral using a transformation, we can use the concept of a double integral over a region in the xy-plane.

First, let's define the transformation T from the uv-plane to the xy-plane, where x = 9u and y = 9v. This transformation scales the coordinates by a factor of 9.

Next, let's find the Jacobian determinant of the transformation. The Jacobian determinant of T is given by the absolute value of the determinant of the matrix of partial derivatives of x and y with respect to u and v. In this case, the matrix is:

J(T) = |[∂x/∂u  ∂x/∂v]|
           |[∂y/∂u  ∂y/∂v]|

Taking the partial derivatives, we have:

∂x/∂u = 9   and   ∂x/∂v = 0
∂y/∂u = 0   and   ∂y/∂v = 9

Therefore, the Jacobian determinant is:

J(T) = |[9  0]|
           |[0  9]|

Taking the determinant, we have:

J(T) = (9)(9) - (0)(0) = 81

Now, we can evaluate the integral by transforming it into the uv-plane. The integral becomes:

∬(9x + 9y) dA = ∬(9(9u) + 9(9v))(J(T)) dA

Since x = 9u and y = 9v, we can substitute these expressions into the integral:

∬(9(9u) + 9(9v))(J(T)) dA = ∬(81u + 81v)(81) dA

Now, we need to find the limits of integration in the uv-plane. The region r in the xy-plane corresponds to a parallelogram in the uv-plane with vertices (-1/9, 2/9), (1/9, -2/9), (3/9, 0), and (1/9, 4/9).

Using these vertices, we can determine the limits of integration for u and v:

u ranges from -1/9 to 1/9
v ranges from 2/9 to 4/9

Therefore, the integral becomes:

∬(81u + 81v)(81) dA = ∫[u=-1/9 to 1/9] ∫[v=2/9 to 4/9] (81u + 81v)(81) dudv

Now, we can evaluate this double integral:

∫[u=-1/9 to 1/9] ∫[v=2/9 to 4/9] (81u + 81v)(81) dudv = (81)(81) ∫[u=-1/9 to 1/9] ∫[v=2/9 to 4/9] (u + v) dudv

Evaluating the inner integral with respect to u, we have:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + vu [v=2/9 to 4/9] dv

Simplifying further, we get:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (vu)(4/9 - 2/9) dv

Now, we can evaluate the inner integral with respect to v:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (vu)(4/9 - 2/9) dv = (81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (vu)(2/9) dv

Simplifying further, we have:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (2/9)u(2/9) dv

Now, we can evaluate the inner integral with respect to v:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (2/9)u(2/9) dv = (81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (4/81)u^2 du

Combining like terms, we get:

(81)(81) ∫[u=-1/9 to 1/9] (1/2 + 4/81)u^2 du

Simplifying further, we have:

(81)(81) ∫[u=-1/9 to 1/9] (85/162)u^2 du

Now, we can evaluate the integral:

(81)(81) ∫[u=-1/9 to 1/9] (85/162)u^2 du = (81)(81)(85/162) ∫[u=-1/9 to 1/9] u^2 du

Integrating u^2 with respect to u, we get:

(81)(81)(85/162) ∫[u=-1/9 to 1/9] u^2 du = (81)(81)(85/162) [u^3/3] from -1/9 to 1/9

Plugging in the limits of integration, we have:

(81)(81)(85/162) [(1/9)^3/3 - (-1/9)^3/3]

Simplifying further, we get:

(81)(81)(85/162) [(1/729)/3 - (-1/729)/3] = (81)(81)(85/162) [2/729]/3

Now, we can simplify this expression:

(81)(81)(85/162) [2/729]/3 = (81)(81)(85/162) (2/729)(1/3)

Finally, evaluating this expression, we get:

(81)(81)(85/162) (2/729)(1/3) ≈ 14.0625

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Answer:840 km/h divided by 60 = 14km/min

3 x 60 = 180

180 + 20 = 200 minutes total

14 x 200 = 2800km

that is a really awkward way of doing it though. really you can just do:

840 x (10/3) = 2800km

Step-by-step explanation:

The local maximum and minimum values of the function are as follows: maximum at (smaller x value), minimum at (larger x value), and there are no saddle points.

To find the local maximum and minimum values of the function, we need to analyze its critical points, which occur where the partial derivatives are equal to zero or do not exist.

Let's denote the function as f(x, y) = -8 - 2x + 4y - x^2 - 4y^2. Taking the partial derivatives with respect to x and y, we have:

∂f/∂x = -2 - 2x

∂f/∂y = 4 - 8y

To find critical points, we set both partial derivatives to zero and solve the resulting system of equations. From ∂f/∂x = -2 - 2x = 0, we obtain x = -1. From ∂f/∂y = 4 - 8y = 0, we find y = 1/2.

Substituting these values back into the function, we get f(-1, 1/2) = -9/2. Thus, we have a local minimum at (x, y) = (-1, 1/2).

There are no other critical points, which means there are no local maximums or saddle points. Therefore, the function has a local minimum at (x, y) = (-1, 1/2) but does not have any local maximums or saddle points.

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Answer:

12.570 meters

Step-by-step explanation:

Answer:

0.410714

Step-by-step explanation:

Dividend ÷ Divisor = Quotient

Therefore, the due date of the note is August 9 adding the number of days in the note's term to the note's date adding the number of days in the note's term to the note's date.

To determine the due date of the note, we need to add the number of days in the note's term to the note's date.

Given:

Note term: 120 days

Note date: April 9

To find the due date, we add 120 days to April 9.

April has 30 days, so we can calculate the due date as follows:

April 9 + 120 days = April 9 + 4 months = August 9

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Answer:

28

Step-by-step explanation:

71.12 divided by 2.54 = 28

Answer:

Using dimensional analysis:

71.12 cm / 2.54 cm/inch = 28 inches

Therefore, 71.12 centimeters is equal to 28 inches.

Based on the formula of the quadratic function y=-x^2+6x-5, we know that its graph is a downward-facing parabola that opens wide, with a vertex at (3,-14), and an axis of symmetry at x=3.

Based on the formula of the quadratic function y=-x^2+6x-5, we can determine several properties of its graph, including its shape, vertex, and axis of symmetry.

First, the negative coefficient of the x-squared term (-1) tells us that the graph will be a downward-facing parabola. The leading coefficient also tells us whether the parabola is narrow or wide. Since the coefficient is -1, the parabola will be wide.

Next, we can find the vertex using the formula:

Vertex = (-b/2a, f(-b/2a))

where a is the coefficient of the x-squared term, b is the coefficient of the x term, and f(x) is the quadratic function. Plugging in the values for our function, we get:

Vertex = (-b/2a, f(-b/2a))

= (-6/(2*-1), f(6/(2*-1)))

= (3, -14)

So the vertex of the parabola is at the point (3,-14).

Finally, we know that the axis of symmetry is a vertical line passing through the vertex. In this case, it is the line x=3.

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Cindy used 48 meters of garland to decorate the rectangular ballroom ceiling by stringing it along the length of 12 meters, then the width of 16 meters, and finally back to the original corner.

To find out how much garland Cindy has used, use the Pythagorean theorem to determine the length of the diagonal, `d`, of the rectangular ballroom ceiling:
`d² = 12² + 16²`

= `d² = 144 + 256`

= `d² = 400`

= `d = √400`

= `d = 20`

Now that we have the length of the diagonal, `d`, we can determine the amount of garland Cindy has used.  To do that, we just need to add up the three distances she has strung the garland:
`12 + 16 + 20 = 48`

Therefore, Cindy has used `48 meters` of garland.

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Answer:

Even with a correlation value of 0.94, it is possible that the relationship could still be better represented by a nonlinear model.