what is the equation of a line that passes thourgh the points (3,6) and (8,4)?


a. y=5/2×-3/2


b. y=5/2×-27/2

c. y=2/5×-24/5

d. y=2/5×+36/5​

Answer:

Step-by-step explanation:

Michelle earns $3 an hour more than Dave.

Answer:

77.3

Step-by-step explanation:

Cos = Adjacent/Hypotenuse

Adjacent = 2.25 & Hypotenuse = 10.25

So that means...

Cos = 2.25/10.25

*When you type in the calculator type Cos-1 (2.25/10.25).

The answer is 77.319....

When you round it, it would become 77.3°.

Hope it's helpful.

Let it be x

Using angle sum theory

\(\\ \sf\longmapsto 50+30+x=180\)

\(\\ \sf\longmapsto 80+x=180\)

\(\\ \sf\longmapsto x=180-80\)

\(\\ \sf\longmapsto x=100\)

Answer:

That is so very true.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the number is x, then we have:

(a) The probability of zero arrivals during the next minute is approximately 0.2231. (b) The probability of z service times less than or equal to a given value can be calculated using the exponential distribution formula.

(a) The probability of zero arrivals during the next minute can be calculated using the Poisson distribution with a rate of 1.5 per minute. Plugging in the rate λ = 1.5 and the number of arrivals k = 0 into the Poisson probability formula, we get P(X = 0) = e^(-λ) * (λ^k) / k! = e^(-1.5) * (1.5^0) / 0! = e^(-1.5) ≈ 0.2231.

(b) In the second part of the problem, the employee serves each customer in 1 minute on average, and the service times follow an exponential distribution. The probability of z service times less than or equal to a given value can be calculated using the exponential distribution. We can use the formula P(X ≤ z) = 1 - e^(-λz), where λ is the rate parameter of the exponential distribution. In this case, since the average service time is 1 minute, λ = 1. Plugging in z into the formula, we can calculate the desired probability.

Note: Since the specific value of z is not provided in the problem, we cannot provide an exact probability without knowing the value of z.

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Answer:

y+-2t^2

Step-by-step explanation:

Therefore , the solution of the given problem of equation comes out to be  9x^3 - 8x^2.

A mathematical equation is a formula that uses the equal sign (=) to connect two statements and express equality. A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the components 3x + 5 and 14 in the equation 3x + 5 = 14 are separated by an equal sign. The equal sign is a crucial part of mathematical formulas, especially equations. Algebra is frequently utilized in equations. Algebra is used in mathematics when it is difficult to determine a precise quantity.

Here,

Polynomial function total

Polynomial functions are those that have a leading degree of three or higher. given the total;

(7x^3-4x^2)+(2x^3-4x^2)

Expand => (7x 3-4 times) + (2x 3-4 times)

= > 7x^3-4x^2 + 2x^3-4x^2

assemble similar terms

=> 7x^3 + 2x^3 - 4x^2 -4x^2

=> 9x^3 - 8x^2

Therefore , the solution of the given problem of equation comes out to be 9x^3 - 8x^2.

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The synergy from the merger is $4,125,000.

To calculate the synergy from the merger, we need to compare the value of Fly-By-Night before and after the acquisition of Flash-in-the-Pan Restaurants. The synergy represents the additional value created through the combination of the two firms.

Given that the purchase of Flash-in-the-Pan Restaurants is expected to increase Fly-By-Night's annual after-tax cash flow by $330,000 indefinitely, we can calculate the present value of this incremental cash flow using the appropriate discount rate of 8 percent.

Present Value of Incremental Cash Flow = Incremental Cash Flow / Discount Rate

Present Value of Incremental Cash Flow = $330,000 / 0.08

Present Value of Incremental Cash Flow = $4,125,000

Now, we can determine the value of Fly-By-Night after the merger by adding the present value of the incremental cash flow to its current market value:

Value of Fly-By-Night after Merger = Current Market Value of Fly-By-Night + Present Value of Incremental Cash Flow

Value of Fly-By-Night after Merger = $23 million + $4,125,000

Value of Fly-By-Night after Merger = $27,125,000

The synergy from the merger can be calculated by subtracting the market value of Fly-By-Night before the merger ($23 million) from the value of Fly-By-Night after the merger ($27,125,000):

Synergy = Value of Fly-By-Night after Merger - Current Market Value of Fly-By-Night

Synergy = $27,125,000 - $23 million

Synergy = $4,125,000

Therefore, the synergy from the merger is $4,125,000. This represents the additional value that would be created through the acquisition of Flash-in-the-Pan Restaurants by Fly-By-Night.

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Answer:

We conclude that the time required to get  a total amount of $6,880.00  from compound interest on a principal of $ 4,400.00  at an interest rate of 2.4% per year  and compounded 4 times per year  is 18 years and 8 months.

Step-by-step explanation:

We know the formula

\(A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}\)

where

Given

Total amount A = $6,880

Principle amount P = $4,400

Interest Rate r =  2.4% = 0.024 per year

Compounded quarterly = n = 4

Thus, the time period can be fetched using  the simplified-derived equation suchs as:

t = ln(A/P) / n[ln(1 + r/n)]

substituting the values

t = ln(6,880.00/4,400.00) / ( 4 × [ln(1 + 0.006/4)] )

t = 18.8 years

Therefore, we conclude that the time required to get  a total amount of $6,880.00  from compound interest on a principal of $ 4,400.00  at an interest rate of 2.4% per year  and compounded 4 times per year  is 18 years and 8 months.

Answer:

The answer is actually 18.7 -.-

Step-by-step explanation:

Based on the information given the average speed for his trip is 64 miles.

Using this formula

d=rt

r=d/t

Where:

r=rate=?

d=distance=512 miles

t=time=8 hours

Let plug in the formula

r=512/8

r=64 miles

Inconclusion the average speed for his trip is 64 miles.

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Answer:

In order to solve this, we need to transform the equation into R = D/T

Plug in the numbers into this equation

R = 512/8

So after we divide these two numbers, we get an answer of 64 mph as Adam's average speed.

If vector u = <-3.5, -1.5> and vector v=<-1.25, 2.25>, the graph given in attachment shows the resulting vector for 2v-u

In mathematics, a vector is an object that has both magnitude and direction. size defines the size of the vector. This is represented by a line with an arrow. The length of the line is the magnitude of the vector and the arrow indicates the direction. It is also known as Euclidean his vector, geometric vector, space vector, or simply "vector".

Given vectors:

vector u = <-3.5, -1.5> and vector v=<-1.25, 2.25>

Now, 2v - u = 2<-1.25,2.25> - <-3.5,-1.5> = <-2.5,4.5> - <-3.5,-1.5>

                                                                = <(-2.5 + 3.5) , (4.5 + 1.5)>

                                                                = < 1 , 6.0>

θ = tan⁻¹ (6/1) = 80.5° ≈ 81 degree

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The scale factor of the dilation of the triangles is 2

From the question, we have the following parameters that can be used in our computation:

The similar triangles

The scale factor of the dilation is the division of the corresponding sides

So, we have

Scale factor = 6/3

When evaluated, we have

scale factor = 2

Hence the scale factor is 2

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Answer:

\(\frac{x-2}{5}\)

Step-by-step explanation:

The inverse function of the function g(x)=5(x-2) is g(x)⁻¹= [( x/5 )+2 )].

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

The inverse function is calculated as:-

y = 5 ( x - 2 )

Replace the variables with each other in the equation.

x = 5 ( y - 2 )

( x/5 ) = y - 2

y = ( x/5 ) + 2

Therefore, the inverse function of the function g(x)=5(x-2) is g(x)⁻¹= [( x/5 )+2 )].

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Unconscious processing is a complex cognitive phenomenon that involves a wide range of mental activities that occur outside of our conscious awareness. It is not simply a group of answer choices or a set of predetermined responses that are guided by habit or well-established routines.

Rather, unconscious processing is a highly nuanced and multifaceted process that is guided by a variety of different factors, including our emotions, our past experiences, our cultural background, and our personal beliefs and values.

At the same time, it is important to note that unconscious processing is not entirely independent of our executive functions or our conscious awareness. While it may be composed of relatively specialized parts, such as our automatic reflexes and basic sensory processing systems, these parts are still intricately connected to the higher-level cognitive processes that govern our decision-making, problem-solving, and goal-oriented behavior.

In short, unconscious processing is a complex and dynamic process that involves a broad range of cognitive and emotional factors, and is intimately intertwined with our conscious awareness and executive functions.

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In a 2 x 2 x 2 factorial design, you need to test a total of seven possible effects: three main effects (A, B, and C) and four interaction effects (A x B, A x C, B x C, and A x B x C).

In a 2 x 2 x 2 factorial design, there are three independent variables, each with two levels. The possible effects to test include main effects and interaction effects.

The main effects are the individual effects of each independent variable on the dependent variable. In this design, there are three main effects to test: the effect of the first independent variable (A), the effect of the second independent variable (B), and the effect of the third independent variable (C).

Interaction effects occur when the effect of one independent variable on the dependent variable depends on the level of another independent variable. In a 2 x 2 x 2 design, there are three possible two-way interaction effects to test: A x B, A x C, and B x C. Additionally, there is one three-way interaction effect to test: A x B x C.

In summary, in a 2 x 2 x 2 factorial design, you need to test a total of seven possible effects: three main effects (A, B, and C) and four interaction effects (A x B, A x C, B x C, and A x B x C).

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\( \: \: \: \: \: \: \: \: \)

\(x = - 1 \\ x = \: 7\)

Step-by-step explanation:

\(2(x - 3 {)}^{2} - 32 = 0\)

\((x - 3 {)}^{2} - 16 = 0\)

\((x - 3 - 4) \times (x - 3 + 4) = 0\)

\((x - 7) \times (x + 1) = 0\)

\(x - 7 = 0 \\ x + 1 = 0\)

\(x = 7 \\ x + 1 = 0\)

\(x = - 1 \\ x = 7\)

\( \: \: \: \: \: \: \: \)

Answer:

$22.50....................

Answer:

363/8π yd²

Step-by-step explanation:

The total area of the circle = πr²

the area of the shaded region = 135/360 × πr² = ⅜ πr² = ⅜ π × 11² = 363/8 π ≈ 136.125 yd²

Answer:

x = 0.37686455

Step-by-step explanation:

Answer: x≈0.37686455

Step-by-step explanation:

\(y=78^{\circ}\) (alternate interior angles theorem)

\(x=78^{\circ}\) (alternate segment theorem)

\(z=24^{\circ}\) (angles in a triangle add to 180 degrees)

Answer:

Step-by-step explanation:

V(x) = x3 + 2x2 - 11x - 12

To factor, you want 3 numbers that multiply to give -12 (the constant term) and add to give 2 (coefficient of the x2 term).  The answer is 4, -3, and 1: (4)(-3)(1) = -12, 4 + (-3) + 1 = 2.  So the volume polynomial factors to:

V(x) = (x+4)(x-3)(x+1)

Now the volume of a rectangular box is:

V = Length*Width*Height = (x+4)(x-3)(x+1)

So let's pick height = (x+1) = 4.5  (you could pick any one of the three factors).

x+1 = 4.5

x = 3.5

Length = (x+4) = 3.5+4 = 7.5

Width = (x-3) = 3.5 - 3 = 0.5

The box's dimensions are 7.5 m by 0.5 m by 4.5 m

Answer:

10 yrs

Step-by-step explanation:

A=P(1+r/n)^nt, P=initial investment, r=annual interest rate,n=number of compounding periods per year, A=amount after t years

For given problem:

P=37000

r=5.5%=.055

n=1

A=62000

..

62000=37000(1+.055)^t

62/37=1.055^t

tlog(1.055)=log(62/37)

Using log keys on calculator:

t=log(62/37)/log(1.055)≈10 yrs

about 13 years

Step-by-step explanation:

Answer:

Add 6 to both sides.

Step-by-step explanation:

Remember you are trying to isolate the variable

It will take 5.01 years for Mantago to repay the money that he would borrow.

Assume that it will take 't' years for Mantago to repay the money that he would borrow.

Here, we use monthly cashflow formula:

\(C=P\times r\times \frac{(1+r)^{12t}}{(1+r)^{12t} - 1}\)

where, P is loan amount

r is ARM(adjustable-rate mortgage) interest rate

C is monthly cashflow

here, R = 7.5%

So, r = 0.075

For monthly payment the interest rate would be r = 0.075/12

i.e., r = 0.00625

P = 10000

C = 200

We need to find the number of years t.

\(200=10000\times 0.00625\times \frac{(1+0.00625)^{12t}}{(1+0.00625)^{12t} - 1} \\\\200=62.5\times \frac{(1.00625)^{12t}}{(1.00625)^{12t} - 1}\\\\ \frac{(1.00625)^{12t}}{(1.00625)^{12t} - 1}=3.2\\\\(1.00625)^{12t}}=[(1.00625)^{12t} - 1]\times 3.2\\\\(1.00625)^{12t}-3.2(1.00625)^{12t}=-3.2\\\\-2.2(1.00625)^{12t}=-3.2\\\\(1.00625)^{12t}=1.4545\)

\(12t=60.13\\\\t=5.01\\\\t \approx 5\)

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