2.5 pts Each week 5 new office phones are installed in a major network company. At the beginning of March, 200 phones had already been installed. Write a linear equation to model this situation. Do not use spaces in the equation.

Use your equation if the company wanted to replace all phones in the building (500 total). How many weeks would it take to finish this project?

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For the given quadratic equation we only have a maximum at y = 18.

Here we have:

[tex]f(x) = -2x^2 - 4x + 16[/tex]

Notice that this is a quadratic equation of negative leading coefficient.

Then we have a maximum at the vertex, and both arms tend to negative infinity as x tends to infinity or negative infinity.

The vertex is at:

x = -(-4)/(2*(-2)) = -1

The maximum is:

[tex]f(-1) = -2*(-1)^2 - 4*(-1) + 16 = -2 + 4 + 16 = 18[/tex]

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Answer:

The answer is 29/42

Step-by-step explanation:

First, let's calculate how many people predicted they would fail. The question states that 65 people took the exam and 23 predicted they would pass, so we can find the number of people that predicted they would fail by the following calculation:

Let FP be the people who predicted they'd fail

65 = 23 + FP

65 - 23 = FP

42 = FP

Now, let's move on to the next part. The question states that a total of 31 people passed the test, from those 18 being the people who predicted they would pass and the rest are people who had predicted they would fail but ended up passing.

Let's set x as the number of people who predicted they would fail but have passed.

31 = 18 + x

31 - 18 = x

13 = x

Since 13 of the 42 FP have passed, we can calculate how many of them failed. Let y be the number of people that predicted to fail and ended up failing:

13 + y = 42

y = 42 - 13

y = 29

Finally, now we have the fraction of those who predicted that they would fail actually did fail and that's 29/42

The statement of stockholders’ equity for Longhorn Corporation is: $62,800

                        Common stock   Retained earning Total stakeholder equity

Beginning balance           $36,000    $17,400        $53,400              

Issuance of common stock  $4,000        -                $4,000

Add net income                          -        $5,400            $5,400

[65,700-(53,000+2,200+5,100)]

Ending balance                      $40,000    $22,800      $62,800

Therefore the statement of stockholders’ equity for Longhorn Corporation is: $62,800.

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Answer:

4.12310562562, 4.23, 4.5

Step-by-step explanation:

The equation of a trigonometric function is

[tex]y = a \sin(bx + c) + d[/tex]

or

[tex]y = a \: cos(bx + c) + d[/tex]

Let define some variables,

D is the midline, this refers to the midpoint of the highest y value and lowest y value. Some textbooks call it the vertical translations but it is the same thing.

A is the amplitude. The amplitude is the distance from the midline to the highest y value. Some distance is non negative, the formula for the amplitude is

[tex] |a| [/tex]

The period is how often the wave repeats itself on a interval.

Period can't be negative so the formula for period is

[tex] \frac{2 \pi}{ |b| } [/tex]

To find the period, look at the extreme points.

The phase shift tells us if the sinusoid have been shifted to the right or left. The formula for the phase shift

[tex]bx + c = 0[/tex]

Solving for x gives us

[tex]x = \frac{ - c}{b} [/tex]

If our x is negative, we have a phase shift to the right

If our x is Positve, we have a phase shift to the left.

Let solve this equation, Let use Sine since sin(0)=0,

The smallest y value here is 0, and the highest is 2, so the amplitude is 1.

[tex]d = 1[/tex]

Next, the distance from the max to the midline is 1, as well the min to the midline is also 1.

So

[tex]a = 1[/tex]

We have minimum at 0, and 8, so our period is 8.

[tex] \frac{2\pi}{b} = 8[/tex]

Solve for b,

[tex] \frac{\pi}{4} = b[/tex]

Plug this in the equation.

[tex]1 \sin( \frac{\pi}{4} x) + [/tex]

[tex]y = \sin( \frac{\pi}{4} x) + 1[/tex]

The graph passes through (4,2) so let see if that holds true for our equation

[tex]2 = \sin( \frac{\pi}{4} (4)) + 1[/tex]

[tex]2 = \sin(\pi) + 1[/tex]

[tex]2 = 0 + 1[/tex]

[tex]2 = 1[/tex]

This doesn't hold true, so we must have a phase shift

Notice that

[tex] \sin( \frac{\pi}{2} ) = 1[/tex]

So if we shift this pi/2 to the right, we can get our equation to be true.

[tex]y = \sin( \frac{\pi}{4} x - \frac{\pi}{2} ) + 1[/tex]

This equation works so our equation is

[tex]y = \sin( \frac{\pi}{4} x - \frac{\pi}{2} ) + 1[/tex]

The value is 1/2

A fraction represents a part of a whole or, more generally, any number of equal parts.

Given:

(5 +(2-1.5)/1*(2))/12

=(5+ 0.5*2)/12

=(5+1)/12

=6/12

=1/2

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[tex]y = 2x {}^{2} + e {}^{ - x {}^{4} } [/tex]

[tex] \frac{dy}{dx} = 4x +( e {}^{ - x {}^{4} } )( - 4x {}^{3} )[/tex]

[tex] \frac{dy}{dx} = 4x - 4x {}^{3} e { }^{ - x {}^{4} } [/tex]

[tex] \frac{dy}{dx} = 4x(1 - x {}^{2} e {}^{ - x {}^{4} } )[/tex]

[tex] \frac{dy}{dx} = 0 \\ 4x = 0 \: \: \: \: \: 1 - x {}^{2} e {}^{ - x {}^{4} } = 0[/tex]

[tex]4x = 0 \\ x = 0 \: \: \: \: \: \: y(0) = 0 + e {}^{0} = 1[/tex]

The price of the washer and the dryer set is $720.

The commission earned by Alice is $36.

Percentage can be described as a fraction an amount expressed as a number out of hundred. Percentage is a measure of frequency.

Price after the mark up = ( + percentage mark up) x cost price

(1  + 0.20) x $600  = $720

Commission earned by Alice = 5% x 720 = $36

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The correct response that would be expected based on the probability information is 164

From the information, there were 352 trials that were made and we're correct 164 times.

Therefore, the correct response that would be expected is 164.

The success rate will be:

= 164/352

= 0.466

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Answer:

its D

Step-by-step explanation:

According to the given conditions, state:

If the fraction is defined, then the denominator cannot equal 0:

Attach the inequality as the domain: x≠0

Reduce the fraction to the smallest term, canceling the greatest common factor: 1/10 = 25/x.

Multiply both sides of the equation by the common denominator:

Simplify the fractions: x = 250

Find the intersection: x = 250

get the result: x = 250

Answer: x = 250

the actual distance would be 250 feet.

Answer:

16.95

Step-by-step explanation:

use a calculator

Answer: y = 3x - 2

Step-by-step explanation:

gradient = (4 - 1)/(2 - 1) = 3/1 = 3

y = 3x + c needs to work for both points

Substitute (1,1) into equation

1 = 3 x 1 + c

c = 1 - 3 = -2

y = 3x - 2

The function for the given situation is f(x)=35.0-0.7x.

Given that, Mark bought 10 pound of two types of candies, caramel candies for $2.80 per pound and chocolate candies for $3.50 a pound.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Now, the function for the given situation is as follows:

If x is the weight of the less expensive candy, the 10-x is the weight of the high expensive candy.

So, f(x)=2.80x+3.50(10-x)

⇒ f(x)=2.80x+35.0-3.50x

⇒ f(x)=35.0-0.7x

Therefore, the function for the given situation is f(x)=35.0-0.7x.

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The mistakes that were made regarding the transformation are:

It should be noted that a transformation simply means the changing of the position of an object

In this case, the transformation is incorrect as he applied the reflection to the pre-image first and used an incorrect angle of rotation around point P.

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Answer:

p=10

Step-by-step explanation:

-7+p=3

+7-7+p=3+7

p=10

Answer:

Hello! The answer to this question is 10.

Step-by-step explanation:

You have to get p by itself so we will add 7 to both sides:

-7 + p = 3

+7        +7

-------------

p = 10

When doing so, we get p = 10.

You can check your work:

-7 + 10 ⇒ 10 - 7 = 3

Therefore, p = 10 is the correct answer.

Answer:

D

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (3, - 2 ) into the partial equation

- 2 = - 6 + c ⇒ c = - 2 + 6 = 4

y = - 2x + 4 ← equation of line in slope- intercept form

Answer:

Step-by-step explanation:

(2x-1)²+8√2xy=4

4y-√8xy-1=1

4y-2√2 x=2

multiply by 4

16y-8√2xy=8

add to first eq.

(2x-1)²+16y=12

or

16y=-(2x+1)²+12

which gives us a downward parabola.

A: Three collinear points are A, T, and B

B: Line BA is another name for line AB

C: Line L is in plane Z

D: line AB is the intersection of planes Z and W

Answer:

step-by-step explanation:

A 7/1 ARM is a mortgage that has a fixed interest rate in the beginning, then switches to an adjustable or variable one. The 7 in 7/1 indicates the initial fixed period of seven years. After that, the interest rate adjusts once yearly based on the index stated in the loan agreement, plus a margin set by the lender.

Answer:

[tex]-6+5i[/tex]

Step-by-step explanation:

[tex]-6+\sqrt{-25}\\\\=-6+5i[/tex]

Answer:

6

Step-by-step explanation:

The mode of a data set, is the value that occurs the most often. There can be multiple modes, if two values have the same amount of frequency in a data set as well as having the highest frequency. So in this case case it appears there is only 1 mode with that being 6, since it appears 3 times.  with no other value appearing this much in the data set.

The area of the square of the leg 6 is 36 square units.

The area of the square of the leg 8 is 64 square units.

The area of the square of the hypotenuse square is 100 square units.

The length of the hypotenuse is 10 units.

Formula Used

Area of square, A = [tex](a)^{2}[/tex]

Here, [tex]a[/tex] is the length of the side of the square.

Pythagoras Theorem is given as,

[tex]h^{2} =p^{2} +b^{2}[/tex]

Here, [tex]h, p, b[/tex] are the hypotenuse, perpendicular, and the base of a right angle triangle respectively.

Area of the Square of the Leg 6

Length of the edge of the square = 6 units

Area of square = 6*6

= 36 square units

Area of the Square of the Leg 8

Length of the edge of the square = 8 units

Area of square = 8*8

= 64 square units

Area of the Hypotenuse Square and the Length of the Hypotenuse

Applying Pythagoras theorem,

[tex]h^{2} = (8)^{2} +(6)^{2}[/tex]

[tex]h^{2} = 64+36[/tex]

[tex]h = \sqrt{100}[/tex]

[tex]h = 10 units[/tex]

Therefore, the area of the hypotenuse square is 100 square units and the length of the hypotenuse comes out to be10 units.

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Answer: in the picture

Step-by-step explanation:

The required points of x where the slope of tangent and secant is equal at boundary points 4 and 9.

Slope is defined as the rate of change or angle at which curve is having inclination or declination.

Since, the curve of 1/2√x defined for interval [4,9]
The curve is of increasing order so the tangent and secant having equal slope only possible at the boundaries of the curve.

Boundary conditions = (4,1) and (9, 1.5)

Equation can be given as,
y = 0.1x + 0.5

Thus, the  required points of x where the slope of tangent and secant is equal at boundary points 4 and 9.

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Answer:

(x+10,y-3)

Step-by-step explanation:

Answer:

60 ways

Step-by-step explanation:

 combination C 4 and 6= (6*5*4*3)/1*2*3=360/6=60 ways

In the case above,  the truth value for the following conditional statement is  Option B: F F → T.

The truth value that was given in the statements are:

So one can write that the truth values of :

p : false

q : false

Then, one need to find the truth value of (p → q)

Note that when as it is written, it means or implies that the truth value of any two statements is false.

If P is true and Q is false then one can say that in every condition, the truth value holds true. So we can then say that p → q: True

In the case above,  the truth value for the following conditional statement is  Option B: F F → T

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The monthly interest payment is 162

Interest, in its most simple form, is calculated as a percent of the principal.

First,

monthly interest rate,

= 0.24/12

= 0.02.

Now,

Average monthly interest,

=0.02×$675

= $13.50.

Thus, the annual interest payments,

= 12×$13.50

= $162

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Answer:

False

Step-by-step explanation:

A rectangle does not have 4 equal sides, it has 2 sets of equal sides.