The average revenue of a TV manufacturing unit is given by r(x)=75x^2-5x^3/2 where x is the number of TVs sold by the firm. Find the total revenue generated by the firm.

Answer:

Step-by-step explanation:

The domain and range of these two functions are identical.

The domain is "all real numbers."

The range is also "all real numbers."

Answer:

Domain of both given functions is the set of real numbers.

Range of both given functions is the set of real numbers.

Step-by-step explanation:

Given functions are

f(x)=5x  

And g(x)= 5x

First, we solve for f(x)

F(x)=5x

Put x=0 then we get

f(x)=0

Now , put x=1  then we get

f(x)= [tex]5\times1=5[/tex]

Put x=2 then we get

f(x)=[tex]5\times2=10[/tex]

Therefore, we can see domain of function f(x) can be set of real numbers and range of function f(x)  can be set of real numbers .Because the function is define at every value of x.

Both function are the same

Therefore , the domain of both function is same and range of both functions is same .

Hence,  the domain of  both functions is the set of real numbers and range of both functions is the set of real numbers.

To build a school;

20 workers -> 18 days.

So 1 worker -> 18/20 days.

So; 12 workers -> (12×18)/20 days.

-> (12×9)/10 days

->10.8 days.

so 10.8 days is your answer.

Hope it helps...

Regards;

Leukonov/Olegion

If 20 workers can build a school in 18 days, how many days will it take 12 workers to build the same school?

In this question we are provided that 20 workers can build a school in 18 days. We are asked to calculate how many days will 12 workers will take to do the same work.

We can solve this question using two methods :

[tex] \small\bf{ Unitary \: Method}[/tex]

20 workers can build a school in 18 days

1 worker can build a school in 20 × 18 days

12 workers can build a school in [tex]\dfrac{20 × 18 }{12}[/tex] = 30 days.

[tex] {{\rule{40mm}{4pt}}}[/tex]

[tex] \small\bf{ Method \: of \: proportion }[/tex]

Let us assume that 12 workers can finish the work in x days.

[tex]\begin{array}{c|c} \bf{Number \: of \: workers }& \bf{Number \: of \: days}\\ 20 & 18 \\ 12 & x\end{array}[/tex]

Ratio of workers = Inverse ratio of days

[tex] \small\sf{ 20 : 12 :: x : 18}[/tex]

Product of mean = Product of extreme

[tex] \small\rm{ 12 \times x = 20 \times 18}[/tex]

[tex] \small \rm{ \dfrac{20 \times 18}{12} = 30 \: days}[/tex]

[tex] \rule{72mm}{5pt}[/tex]

Answer:

8%

Step-by-step explanation:

For this case we have that by definition, the distance between two points is given by:

[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}\\(x_ {1}, y_ {1}) :( 2,2)\\(x_ {2}, y_ {2}) :( 5,5)[/tex]

Substituting the points:

[tex]d = \sqrt {(5-2) ^ 2 + (5-2) ^ 2}\\d = \sqrt {(3) ^ 2 + (3) ^ 2}\\d = \sqrt {9 + 9}\\d = \sqrt {18}\\d = 3 \sqrt {2}[/tex]

ANswer:

[tex]d = 3 \sqrt {2}[/tex]

Answer:

To the right we have 62.6 while to the left we have 49.4

Step-by-step explanation:

A normal distribution is usually symmetric with respect to the mean. The mean of the distribution is also the mode as well as the median.

The general formula for points that lie n standard deviations away from the mean on either sides of the mean is given by the formula;

mean ± n(σ)

where σ is the standard deviation of the distribution;

Two standards deviations from the mean imply that n = 2;

56 ± 2(3.3)

56 ± 6.6

To the right we have 62.6 while to the left we have 49.4

Answer:

The measure of angle x is [tex]64.4\°[/tex]

Step-by-step explanation:

To find the measure of angle X, apply the law of cosines

The law of cosines states that

[tex]c^{2}=a^{2}+b^{2}-2(a)(b)cos(C)[/tex]

In  this problem we have

[tex]a=19\ cm[/tex]

[tex]b=25\ cm[/tex]

[tex]c=24\ cm[/tex]

[tex]C=x\°[/tex]

substitute

[tex]24^{2}=19^{2}+25^{2}-2(19)(25)cos(C)[/tex]

[tex]576=986-950cos(C)[/tex]

[tex]cos(C)=(986-576)/950[/tex]

[tex]C=arccos[(986-576)/950]=64.4\°[/tex]

Therefore

The measure of angle x is [tex]64.4\°[/tex]

k(3)=13(3)-2

k(3)= 39-2

Answer is k(3)= 37

ANSWER

[tex]k(3) = 37[/tex]

EXPLANATION

The given expression is

[tex]k(t) = 13t - 2[/tex]

We want to find k(3).

We substitute t=3 into the expression to get:

[tex]k(3) = 13(3) - 2[/tex]

We multiply out to get,

[tex]k(3) = 39- 2[/tex]

Simplify to get,

[tex]k(3) = 37[/tex]

Answer:

Part 1) The x-intercept is the point (-5,0)

Par 2) The y-intercept is the point (0,-17.5)

Step-by-step explanation:

step 1

Find the x-intercept

we know that

The x-intercept is the value of x when the value of y is equal to zero

Observing the table

For x=-5, y=0

therefore

The x-intercept is the point (-5,0)

step 2

Find the equation of the line

Find the slope m

we have

(-7,7) and (-5,0)

[tex]m=(0-7)/(-5+7)\\ m=-3.5[/tex]

Find the equation of the line into point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-3.5[/tex]

point (-5,0)

substitute

[tex]y-0=-3.5(x+5)[/tex]

[tex]y=-3.5(x+5)[/tex]

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

For x=0

[tex]y=-3.5(0+5)[/tex]

[tex]y=-17.5[/tex]

therefore

The y-intercept is the point (0,-17.5)

Answer:

360°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 4, hence

sum of interior angles = 180° × 2 = 360°

Answer:

(D same size and same shape)​

Step-by-step explanation:

Congruent means the same size and shape.

Similar means the same shape, but not necessarily the same size

Answer:

The answer is : (D same size and same shape)​

Step-by-step explanation:

Two shapes or figures are called congruent, when they are identical. When the angles are equal in degrees, they are called congruent angles and when sides are congruent, this means they have the same length.Two polygons are congruent if they have the same size and shape or if their corresponding sides and angles are equal.

Therefore, option D is correct.

Answer:

c

Step-by-step explanation:

the formula is [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1}}[/tex]

When we plug that in we get [tex]\frac{-3-2}{6- (-4)} = \frac{-5}{10} = -\frac{1}{2}[/tex]

Hope this helps!

Answer:

The correct answer is  last option

Cos(55) = 11/x

Step-by-step explanation:

Points to remember

Trigonometric ratios

Sin θ = Opposite side/Hypotenuse

Cos θ = Adjacent side/Hypotenuse

Tan θ = opposite side/Adjacent side

From the figure we can see a right angled triangle, with one angle is 55 degree, one side is 11 and hypotenuse is x

To find the correct trigonometric formula

Here we have adjacent side of angle 55

Cos 55 = Adjacent side/Hypotenuse

Cos 55 = 11/x

Therefore the correct answer is last option

The system of equations to represent the concession stand sales situation is 3H + 4B = 184 for the total sales, and H = B + 10 for the quantity relationship, where H is the number of hot dogs sold, and B is the number of burgers sold.

To represent this situation with a system of equations, let's denote the number of hot dogs sold as H and the number of burgers sold as B. According to the problem, hot dogs are sold at $3 each and burgers at $4 each, and the stand made $184 in total. Also, we are told that 10 more hot dogs than burgers were sold at the game.

We can create two equations to represent this scenario:

These two equations form the system that can be solved to find the number of hot dogs and burgers sold.

Answer:

The second answer is correct.

Step-by-step explanation:

Answer:

One solution

Step-by-step explanation:

Expanding the equation, we get

-2w-12-6w=4w+12

Subtracting 4w from both sides, we get

-12w-12=12

Now adding 12 to both sides,

-12w=24

Solving for w, we get

w=-2

So there is only one solution to the equation.

Answer:

7.04 trillion = 7.04 x 10¹²

Step-by-step explanation:

Answer: 7.04 x 10^12

Step-by-step explanation:

Just took the test :)

Answer:

1/4

Step-by-step explanation:

because if you use the process of breaking down the numbers they will end up going down to simplest form.

Answer:

3/12 = 1/4

Step-by-step explanation:

If we know 12 is equal to a fraction with the denominator of 4, we can divide 12 by 4 and get 3. This means we must also divide the numerator by 3 to get 3/3 = 1. Another way to solve this is to cross multiply. If 3/12 = _/4, we multiply the numerator of the first fraction by the denominator of the second fraction. Then, we get 12. Divide the 12 by the denominator of the first fraction to get 12/12. This will give you an answer of 1 as well.

Answer: 9

Step-by-step explanation:

M=3 and the equation is 3m so your going to multiply. So the equation would be 3*3 and 3*3=9 so that's your answer

The slope is [tex]\frac{3}{4}[/tex] and x-intercept is [tex]\frac{8}{3}[/tex] and y-intercept is -2 of the linear equation [tex]y=\frac{3}{4}x-2[/tex].

Slope intercept form is one of the forms used to calculate the equation of a straight line.

i.e. y = mx + b

Here, m= slope and y = intercept ,

We have,

[tex]y=\frac{3}{4}x-2[/tex]

Now,

Compare the given equation with the slope intercept form,

i.e.

y = mx + b

[tex]y=\frac{3}{4}x-2[/tex],

So,

Slope [tex](m)=\frac{3}{4}[/tex],

Now,

To know, the x-intercept,

put y = 0,

i.e.

[tex]0=\frac{3}{4}x-2[/tex]

⇒[tex]\frac{3}{4}x=2[/tex]

We get,

[tex]x=\frac{8}{3}[/tex],

Now,

To know, the y-intercept,

put x = 0,

i.e.

[tex]y=\frac{3}{4}*0-2[/tex]

We get,

y = -2

Hence, we can say that the slope is [tex]\frac{3}{4}[/tex] and x-intercept is [tex]\frac{8}{3}[/tex] and y-intercept is -2 of the linear equation [tex]y=\frac{3}{4}x-2[/tex].

To know more about Slope intercept forms click here

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Final answer:

The slope of the equation y = 3/4x - 2 is 3/4, and the y-intercept is -2.

Explanation:

The linear equation given is y = 3/4x - 2. In this equation, the coefficient of x represents the slope and the constant term represents the y-intercept. Therefore, the slope of the line is 3/4 and the y-intercept is -2. The slope indicates that for each unit increase in x, y increases by 3/4, while the y-intercept tells us that when x is 0, the value of y is -2, indicating the point at which the line crosses the y-axis.

Distributive property means that you must multiply the number directly outside the parentheses to all the numbers inside the parentheses

Look at the image below for the work!

Hope this helped!

Using the Distributive Property to expand and evaluate an expression.

Given expression: (5 + 1)3

Step 1: Apply the Distributive Property to expand the expression:  (5 + 1)3 = 5 x 3 + 1 x 3

Step 2: Evaluate the expression: (5 + 1)3 = 15 + 3 = 18

Answer:

The desired equation is y = -2x - 4

Step-by-step explanation:

The general slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Starting from that, substitute the given values for m, x and y and calculate b:

6 = -2(-5) + b.  Then 6 = 10 + b, and b = -4.

The desired equation is y = -2x - 4.

Answer: -5, and 5

Step-by-step explanation: an absolute value can only be positive. So -5 and 5 are the only answers that will give you 5.

Answer:

B and D.

Step-by-step explanation:

–15

–5

0

5

15

Absolute Value  Assignment

Finding Absolute Value

Answer:

y = 5x + 3

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 = 5, hence

y = 5x + c

The line passes through the y- axis at (0, 3) ⇒ c = 3

y = 5x + 3 ← equation of line

Answer:

False

Step-by-step explanation:

The equation x = c represents the equation of a vertical line parallel to the y- axis.

The equation y = c represents the equation of a horizontal line parallel to the x- axis

In both cases c is a constant

Hence x = - 2 is not parallel to the x- axis

Answer:

The length side of the original square banner was 9 ft

Step-by-step explanation:

Let

x-----> the length side of the original square banner

we know that

The new area of the banner is equal to

[tex]91=(x+4)(x-2)[/tex]

Solve for x

[tex]91=(x+4)(x-2)\\ \\91=x^{2}-2x+4x-8\\ \\x^{2}+2x-99=0[/tex]

Solve the quadratic equation by graphing

The solution is x=9 ft

see the attached figure

To determine the length of the original square banner, we can set up an equation using the given information and solve for the side length.

To solve this problem, let's first represent the length of the original square banner as x. According to the question, 4 feet is added to the width, so the width becomes x + 4. Also, 2 feet is subtracted from the height, so the height becomes x - 2. The area of a square is calculated by multiplying the side lengths, so we have (x + 4)(x - 2) = 91.

Expanding the equation, we get x² + 2x - 8 = 91. Rearranging the equation, we have x² + 2x - 99 = 0. This is a quadratic equation that can be solved by factoring, completing the square, or using the quadratic formula.

By factoring, we find (x + 11)(x - 9) = 0. So, x = -11 or x = 9. Since we cannot have a negative length for a banner side, we discard x = -11. Therefore, the length of the side of the original square banner is 9 feet.

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Answer:

Step-by-step explanation:

[tex](f\circ f)(x)=f\bigg(f(x)\bigg)\\\\f\bigg(f(3)\bigg)\\\\\text{Calculate}\ f(3):\\\\f(3)=3^2-3=9-3=6\\\\f\bigg(f(3)\bigg)=f(6)=6^2-6=36-6=30[/tex]

ANSWER

The missing probability is 0.15

EXPLANATION

From the given probability distribution table.

P(1)=0.30

P(2)=0.40

P(3)=0.15

P(4)=?

For for this to represent a probability distribution function,then the sum of all the probabilities must be equal to 1.

P(1)+P(2)+P(3)+P(4)=1

This implies that,

0.30+0.40+0.15+P(4)=1

0.85+P(4)=1

P(4)=1-0.85

P(4)=0.15

Therefore the missing probability is 0.15

The answer is B, if you substitute x with 0 1 or 2 the result will always be 0

ANSWER

[tex]f(x) ={x}^{3} - 3 {x}^{2} + 2x[/tex]

EXPLANATION

If the polynomial function has zeros at 0,1 and 2

Then the polynomial can be written in factored form as:

F(x)=x(x-1)(x-2)

We expand to get,

[tex]f(x) =x({x}^{2} - 3x + 2)[/tex]

Expand further to obtain:

[tex]f(x) ={x}^{3} - 3 {x}^{2} + 2x[/tex]

The polynomial in descending powers of x is said to be in standard form .

The last choice is correct.

Answer:

500 Elm: Cafe

524 Elm: Grocery

538 Elm: Boutique

544 Elm: Dance studio

Step-by-step explanation:

We know that the dance studio has the highest address, so 544.

For the others let's examine the possibilities.

The boutique is between the cafe and the studio, that means the following are possible:

Boutique can be at either 524 or 538, cannot be at 500 (since cafe has to be on the its left.

Cafe can be 500 or 524, cannot be 538 since boutique has to be between cafe and studio.

The grocery is between the cafe and boutique. Meaning the grocery cannot be 500 nor 538, since it has to be in the middle of the 3 remaining businesses.  So, grocery is at 524.

Meaning the Cage is at 500 and the boutique is at 538.

Answer:

B

Step-by-step explanation:

On edge