COMPUTER TABLETS Last year, an office supply store sold 220 computer

tablets for $420 each. This year its manager is considering reducing the

price to increase sales. She estimates that for each $12 decrease in price,

the store will sell 20 additional tablets.


a. Define variables and write a function to represent the situation.


b. How much should the store charge for each tablet to maximize its profit?


c. Find the domain and range in the context of this situation

Answer: R=(320,380)

Step-by-step explanation:

if mia cannot work more than 5 hours overtime a week

then x<5

or x=5 (maximum)

so the domain is (0,5)

and the range will be y when x is (0,5)

so the range is(320,380)

Answer: 5.4 inches

Step-by-step explanation:

The area of a triangle is the base x height/2.

The red is telling you the triangle is 2.7 inches tall, and the black is telling you that the base is 4 inches.

That means the answer is 4 * 2.7/2 = 5.4

Answer: 3x + y = 2

Step-by-step explanation: Take the 3x and put it in the beginning then write 2  + y = 2. It's because we first must put the number that has an x on it then put the letter y, so 3x + y = 2.

Answer:

y=2-3x in standard form is y =3x+2

Step-by-step explanation:

because we moved the 2 to the other side and when 2 crosses a negative sign it becomes minus and when minus 3x crosses a negative sign it becomes plus becos minus times minus is plus.

Answer:

B

Step-by-step explanation:

A C D are functions but B is not a function

The interval for the inequality is (5, ∞].

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

-11m <= -55

Now, solving the inequality

-11m ≤ -55

Divide both side by 11

-11m/ 11 ≤ -55/ 11

-m ≤ -5

m≥ 5

Hence, the interval for the inequality is (5, ∞]

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Answer: P=28 units

Step-by-step explanation:

The perimeter is the sum of the lengths of all the sides of a polygon

1) Let the perimeter of a square is P₁

Since a square has four sides perimeter of a square is:

                                           P₁=4(x+1)

2) Let the perimeter of a triangle is P₂

A triangle has three sides perimeter of a triangle is:

P₂=(x+2)+(x+3)+(x+5)

P₂=x+2+x+3+x+5

P₂=3x+10

Since the square and the triangles have the same perimeter

P₁=P₂

4(x+1)=3x+10

4(x)+4(1)=3x+10

4x+4=3x+10

4x+4-4=3x+10-4

4x=3x+6

4x-3x=3x+6-3x

x=6

Hence,

P=4(x+1)

P=4(6+1)

P=4(7)

P=28 units

The solution for the inequality is:

-20 < x < 2

And the graph of the solution set can be seen below.

Here we have the inequality:

|x + 9| - 9 < 2

If we add 9 in both sides, we will get:

|x + 9| < 2 + 9

|x + 9| < 11

Now we can decompose the absolute value in a compound inequality:

-11 < x + 9 < 11

Now we can subtract 9 in the whole inequality to get:

-11 - 9 < x < 11 - 9

-20 < x < 2

The graph of this inequality is the one you can see below.

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The equation of the parabola that has its x-intercepts at (-1.6, 0) and (-3.2, 0) and its y-intercept at (0, 25.6) is  5x² + 8x - 25.6

The x intercept refers to the value of x when y = 0 this otherwise known as the roots of the polynomial equation.

The intercept form of parabolic equation is

y = a(x - p)(x - q)

where

p and q are roots

a = constant

writing the equation at (-1.6, 0), (-3.2, 0)

y  = a( x + 1.6 ) ( x + 3.2 )

passing through point (0, 25.6)

25.6  = a( 0 + 1.6 ) ( 0 + 3.2 )

25.6 = 5.12a

a = 5

substituting into the equating gives

y = a(x - p)(x - q)

y = 5( x + 1.6 ) ( x + 3.2 )

expanding the equation gives

= 5(x² + 3.2x - 1.6x - 5.12)

= 5(x² + 1.6x - 5.12)

= 5x² + 8x - 25.6

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Answer:

Joshua is correct

Step-by-step explanation:

6x+7+(-2x)+4

6x+7-2x+4

4x+7+4

4x+11

Hopes this helps please mark brainliest

Answer:

Joshua, you can’t simplify/add because they aren’t like terms

Answer:

a = 32.3 m/s^2

F = 64.6 N

Step-by-step explanation:

a = v^2 / r

a = 10^2 / 3.1

a = 32.3 m/s^2

F = ma

F = 2 * 32.3

F = 64.6 N

Answer: A, D, F

The guy above me is wrong.

The height of telephone pole is 56.44 ft.

Given,

length of shadow =12 ft

angle of at which sunray strikes the ground =78°

Le the height of telephone pole be 'x'

From figure,

We can use trigonometric ratios to find the height of pole,

[tex]tan\theta=\frac{opposite\ side}{adjacent\ side}\\\\tan78 \textdegree=\frac{x}{12}\\\\4.704=\frac{x}{12}\\\\h=4.704*12\\\\h=56.448[/tex]

Thus, the telephone pole is 56.448 ft high.

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Your question is incomplete, please complete the question.

0.16 will be the Sample Proportion / Parameter.

Given info,

A randomly selected sample of 1,000 college students was asked whether they had ever used the drug Ecstasy. Sixteen percent (16% or 0.16) of the 1,000 students surveyed said they had.

To know which one of the following statements about the number, 0.16 is correct,

This value, 16% = 0.16 would be the sample proportion,

[tex]\hat p[/tex], since it originated from the sample.

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The dimensions of A and B are

[tex]A= LT^{-1}[/tex]

[tex]B = LT^{-1/2}[/tex]

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be x

x = At + B√2t

where x is the displacement

t is the time taken

So , the dimension of x will be L

And , the dimension of t will be T

Now ,

The equation is x = At + B√2t

So , the first term At should have dimension of L

And , the second term B√2t should have dimension of L

Therefore , the equation will be

So , The dimension of A will be

[tex]A= LT^{-1}[/tex]

And the dimension of B will be

[tex]B = LT^{-1/2}[/tex]

Hence , The dimensions of A and B are

[tex]A= LT^{-1}[/tex]

[tex]B = LT^{-1/2}[/tex]

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The probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.3 is 0.16%.

The normal distribution is a type of probability function that describes how a variable's values are distributed. Since the majority of the observations cluster around the curve's middle peak, it is symmetric. In both directions, the probability for values of the distribution that are far from the mean.

Given that the fracture strength of tempered glass averages 14.1 (measured in thousands of pounds per square inch) and has standard deviation 2.

We have to determine what is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.3?

We that μ = 14.1 σ = 2 n = 100 δ = 2/√100 = 0.2

This probability is 1 subtracted by the p-value of Z when X = 14.3. So

Z = (x-μ)/σ

By the Central Limit Theorem

Z = (x-μ)/δ

Z = (14.3 – 14.1)/0.2

Z = 0.2/0.2

Z = 1

Z =1 has a p-value is 0.8413

= 1 - 0.8413 = 0.1587

Therefore 0.16% is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.3.

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Answer:

5

Step-by-step explanation:

180-20x+10 equals the inside angle

180-14x-8x equals the inside angle

20x+10=14x+8x

10=22x-20x

10=2x

5=x

The situations that can be modeled by uniform distribution include;

Option 2) is: When each discrete value is

equally likely to occur.

Option 3) is:  When each value of a continuous random variable is equally likely to occur.

Since each value has an equal chance of occurrence, thus this situation can be  modelled by Uniform distribution.

Since each value of a continuous random variable is equally likely to occur, that it follows a continuous uniform distribution.

A uniform distribution is a type of probability distribution in statistics in which all outcomes are equally likely. A deck of cards has uniform distributions because the chances of drawing a heart, a club, a diamond, or a spade are all equal. When you sample a random element, you do so according to some distribution.

The term "uniformly" refers to sampling from a uniform distribution, i.e., from a set in which drawing each element is equally likely. In statistics, it is a type of probability distribution in which every possible outcome has an equal chance of occurring. Because each variable has an equal chance of being the outcome, the probability is constant.

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If a park ranger, on top of a 200-­‐foot tower, spots a wolf at an angle of depression of 14°. The distance of the wolf from the base of the tower is:  A. 802.2 ft.

Making use of Tan to solve for x

Let x represent the distance between the tower and the wolf

Hence,

Tan 14° =200/x

Cross multiply

x =  200/Tan 14°

x = 200 / 0.2493

x = 802.2 ft

Therefore the correct option is A.

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The measure of angle E is 121 degrees

The length of the side AB = The length of the side DE

The length of the side BC = The length of the side EF

The length of the side AC = The length of the side DF

The three sides of the triangle ABC is equal to the three sides of the triangle DEF.

Therefore the triangle ABC and triangle DEF is congruent

Therefore,

Angle B = Angle E

96 + y = 6y - 29

6y -y = 96 + 29

5y = 125

y = 125 / 5

y = 25

Angle E = 6y - 29

= 6×25 - 29

= 150 - 29

= 121 degrees

Hence, the measure of angle E is 121 degrees

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The speed of Melitta in miles per hour is 3 mph .

In the question ,

it is given that

the distance covered by Melitta for morning exercise in 3/4 of an hour =  [tex]2\frac{1}{4}[/tex] mile =

we need to convert the mixed fraction to normal fraction ,

So , [tex]2\frac{1}{4}[/tex] = (2*4 + 1)/4 = (8 + 1)/4 = 9/4 mile

we know that the speed [tex]=[/tex] distance / time

So , Speed of Melitta = (distance covered) / (time taken )

Speed  = (9/4)/(3/4)

= 9/4 × 4/3

= 3 miles per hour .

Therefore , The speed of Melitta in miles per hour is 3 mph .

The given question is incomplete , the complete question is

Melitta found out that if she walk really fast during her morning exercise, she can cover [tex]2\frac{1}{4}[/tex] mile in 3/4 of an hour. How fast is she walking in mile per hour ?

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For the exponential growth and the problems based on decay the independent variable is always time .

As given in the question,

Function based on exponential growth and decay problems is represented by :

f(t) = A[tex]e^{kt[/tex]

Function (f) is the dependent variable which depends on time t.

A is the amount for the given model which may vary according to the time.

e is the exponential function which is constant as per the value of time.

t is the time which is not depends on any of the factors given . Time is considered as independent variable.

Therefore, for the exponential growth and the problems based on decay the independent variable is always time.

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Answer:

Step-by-step explanation:

Amber coaches both sports for 7 hours each day

v = volleyball hours

s = soccerball hours

7 hours in total, in which soccerball is 1 hour more than volleyball:

v + s = 7

s = v + 1

plug in v + 1 for s

v + s = 7

v + (v + 1) = 7

simplify

v + v + 1 = 7

2v + 1 = 7

2v + 1 (-1) = 7 (-1)

2v = 6

2v/2 = 6/2

v = 6/2

v = 3

Plug in 3 for v for one of the equations.

s = v + 1

s = (3) + 1

s = 4

Amber coaches 3 hours for volleyball, and 4 hours for soccer, making a total of 7 hours becuase 4+3 equals 7

hope this help :DDDDD

The function f(x) = 1/9x² + 12x + 7 has zeros or solution as x = -0.61

Roots of quadratic equation is the values of variables satisfying the given quadratic equation are called its roots. In other words, x = α is a root of the quadratic equation f(x), if f(α) = 0. The real roots of an equation f(x) = 0 are the x-coordinates of the points where the curve y = f(x) intersect the x-axis.

The roots of the quadratic function or zeros of the function is the actual solution of the quadratic function.

In the given function f(x) = 1/9x² + 12x + 7 has roots of -0.608≅ -0.61

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Answer:

13. [tex]y=-3x[/tex]

14. [tex]y=\frac{2}{5} x+\frac{23}{5}[/tex]

15. [tex]y=4x+3[/tex]

16. [tex]y=-0.5x+6[/tex]

Step-by-step explanation:

Step 1: Point Slope Form

Step 2: Plug in and isolate y to one side (Standard Form)

   13. m = -3 and point: (0,0)

   14. m = 2/5 and point: (6,7)

   15. m = 4 and point: (-2,-5)

   16. m = -0.5 and point: (0,6)

$80,000 is subject to a $4433 state income tax.

Taxes are sums of money that citizens are required to pay in accordance with their income, the value of their property, and other factors. These sums of money are used to fund the government's activities. A taxpayer is a natural person, business, or other entity that must pay taxes. The government may provide identity or reference numbers to individuals or businesses as modern taxpayers. One who pays taxes is often referred to as a "taxpayer".

Given,

The sum of the taxes owed in each bracket is the total amount owed in taxes.

2%×$3000 +3%×(8000 -3000) +5%×(17000 -5000) +5.75%×(80000 -17000)

= 60 +150 +600 +3622.5

= $4432.50

≈ $4433

$80,000 is subject to a $4433 state income tax.

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The expression is f(x) = $0.95x+$9.50

From the question, we have

A cell phone company charges $9.50 per month to rent a cell phone and $0.95 per minute.

f(x) = $0.95x+$9.50

Addition:

The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts, Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.

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The complete table using the given function y = 3x²- 12x + 6 is below

x     y

1     -3

3     -3

0      6

4      6

The table is competed by using the function and solving for y at different times

The function given to complete the table is

y = 3x²- 12x + 6

substituting the different values of x gives y values

at x = 1

y = 3(1)²- 12 * 1 + 6 = -3

at x = 3

y = 3(3)²- 12 * 3 + 6 = -3

at x = 0

y = 3(0)²- 12 * 0 + 6 = 6

at x = 4

y = 3(4)²- 12 * 4 + 6 = 6

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Answer:

4d + 5 ≥ 13

Step-by-step explanation:

1. 4d + 5 ≥ 13

-5 -5

4d ≥ 8

4d/4 = d

8/4 = 2

d=2

4x2+5 =13

13≥13

2. 7d - 2 < 12

+2 +2

7d < 14

7d/7= d

14/7 = 2

d=2

7x2-2 = 12

12<12