A rectangular whiteboard has an area of 108 square inches. The width of the whiteboard is 9 inches. What is the perimeter
of the whiteboard?

The table that represents a linear function is table B.

A general linear function can be written as:

y = ax + b

Here we can see that for a increase of 1 unit in x, we have a constant increase/decrease of y (which is equal to a).

Only with that we can rule out the tables A, C, and D (C and D because we can see increases and decreases in the y-values).

And table A can be discarded because we have increases of 1 unit in x, but the increases in y aren't equal.

So the only remaining option is B.

Where we can see that as x increases, also does y.

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Answer:

The cost function is simply the initial cost plus the manufacturing cost.

C(x)=500+20x-5x^3/4+0.01x^2

The demand function was given to us.

p(x)=320-7,7x

The revenue function is simply x multiplied by the demand function.

R(x)=xp(x)=320x-7.7x^2

We find that when 20 planes are produced, that profit is currently maximized

We know that to maximize profit, marginal revenue must equal marginal cost.

C'(x)=20-15/4x^-1/4+0.02x

R'(x)=320-15.4x

x=19,57

We find that when 20 planes are produced, that profit is currently maximized.

Step-by-step explanation:

An aircraft manufacturer wants to determine the best selling price for a new airplane. The company estimates that the initial cost of designing the airplane and setting up the factories in which to build it will be 500 million dollars. The additional cost of manufacturing each plane can be modeled by the function: , where x is the number of aircraft produced and m is the manufacturing cost, in millions of dollars. The company estimates that if it charges a price p (in millions of dollars) for each plane, it will be able to sell  planes.

(a) Find the cost, demand, and revenue functions.

(b) Find th eproduction level and the associated selling price of the aircraft that maximizes profit.

Using the length formula we know that the length of the given arc is 30.144 miles.

In mathematics, an arc is a portion of the boundary of a circle or curve. It is sometimes referred to as an open curve.

The measurement around a circle that determines its edge is called the circumference, often known as the perimeter.

So, the formula to find the length of the arc is:

Length of an Arc = θ × r

Now, insert values and calculate as follows:

Length of an Arc = θ × r

Length of an Arc = 4π/5 × 12

Length of an Arc = 4π/5 × 12

Length of an Arc = 12.56/5 * 12

Length of an Arc = 2.512 * 12

Length of an Arc =  30.144

Therefore, using the length formula we know that the length of the given arc is 30.144 miles.

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Steps to solve:

x - 1 = 4

~Add 1 to both sides

x = 5

Best of Luck!

The equation of the perpendicular line is \(y=-\frac{2}{3}x+4\)

The equation is defined by 2y = 3x + 2

Rewrite the equation in the form y = mx + c

\(y=\frac{3}{2}x + 1\)

The slope, m = 3/2

The y-intercept, c = 1

The equation perpendicular to the given line will be of the form:

\(y-y_1=\frac{-1}{m}(x-x_1 )\)

Substitute \(x_1=3, y_1=2, and m=\frac{3}{2}\) into the equation above

\(y-2=\frac{-2}{3} (x-3)\\\\y-2=-\frac{2}{3}x+2\\\\y=-\frac{2}{3}x+4\)

Therefore, the equation of the perpendicular line is \(y=-\frac{2}{3}x+4\)

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The equivalent expression to the expression (m-²n-3)-4 is  (m-²n- 7).

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The given expression is (m -² n - 3) - 4. The expression will be solved as below,

E = (m -² n - 3) - 4

E = (m -² n - 3 - 4 )

E = (m -² n - 7

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Answer: d=353.7°

Step-by-step explanation: edge 2020

Answer:

d

Step-by-step explanation:

Comparing the graphs we understand :

⇒ g(x) is equal to f(x) when shifted down 2 units

===========================================================

Hence :

⇒ g(x) = f(x) - 2

⇒ g(x) = (x + 7)² - 2

Answer:

B)

Step-by-step explanation:

4y = 3x + 5 has a slope of 3/4

4y = 3x - 1 has a slope of 3/4

parallel lines have equal slopes

The equation of a straight line that is parallel to the line 4y = 3x + 5 is B. 4y = 3x - 1.

To find an equation of a straight line that is parallel to the given line 4y = 3x + 5, we need to identify the equation that has the same slope as the given line

The given line is in the form 4y = 3x + 5. We can rewrite this equation in slope-intercept form (y = mx + b) by dividing both sides by 4:

y = (3/4)x + 5/4.

The slope of the given line is (3/4).

To find a parallel line, we need to choose an equation with the same slope of (3/4). Among the options provided:

A. y = 3x + 5 - The slope of this line is 3, not (3/4), so it is not parallel.

B. 4y = 3x - 1 - This line has a slope of (3/4), making it parallel to the given line.

C. 3y = 4x - 3 - The slope of this line is (4/3), not (3/4), so it is not parallel.

D. 4y = x + 5 - The slope of this line is (1/4), not (3/4), so it is not parallel.

Therefore, the equation of a straight line that is parallel to the line 4y = 3x + 5 is B. 4y = 3x - 1.

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The test statistic based on the probability illustrated is -3.22.

Based on the information, the test statistic will be:

= (0.4 - 0.5)/[✓0.5(1 - 0.5)/260]

= -3.22

The p value using the distribution table is 0.0012.

The conclusion is to reject the null hypothesis as there's sufficient evidence to warrant rejection.

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Answer:

Your answer is x = 47.

Step-by-step explanation:

First, you need to move the constant to the right-hand side and change its sign.

4x = 180 + 8

Now, you need to add the numbers.

4x = 188

Last but not least, you need to divide both sides of the equation by 4, which gets you to:

x = 47

Based on the information provided, the sum of all the labeled angles is 235° (option b).

To calculate the sum of all the labeled angles we must add the different values of each labeled angle as shown below:

80° + 92° + 40° + 23° = 235°

According to the above, it can be inferred that the correct option is B because the result of the sum of the values coincides with this sum.

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The solution set for the inequality is x < 2. Among the given options, the value that is included in the solution set is 0.

To determine which value is included in the solution set for the inequality statement -3(x-4) > 6(x-1), we need to solve the inequality for x.

Starting with the given inequality:

-3(x - 4) > 6(x - 1)

First, distribute -3 and 6 to the terms inside the parentheses:

-3x + 12 > 6x - 6

Next, combine like terms by subtracting 6x from both sides and adding 6 to both sides:

-3x - 6x > -6 - 12

-9x > -18

To isolate x, divide both sides of the inequality by -9. Remember that when dividing by a negative number, we need to reverse the inequality sign:

x < (-18) / (-9)

x < 2

Therefore, the solution set for the inequality is x < 2. Among the given options, the value that is included in the solution set is 0.

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Answer:

17

Step-by-step explanation:

65% can be simplified to \(\frac{13}{20}\). Multiplying \(\frac{13}{20}\) by 25 gets 16.25 but since 16 would get you under 65%, you would need to correctly answer 17 questions.

We are given –

We know that–

\(\qquad\)\( \purple{\bf\longrightarrow Area_{(Rectangular)} = Length \times Breadth} \)

\(\qquad\)\( \sf \longrightarrow 92 = 11.5 \times Breadth \)

\(\qquad\)\( \sf \longrightarrow Breadth = \cancel{\dfrac{92}{11.5}}\)

\(\qquad\)\( \purple{\bf \longrightarrow Breadth = 8 \: mm}\)

Now, Perimeter of rectangular –

\(\qquad\)\( \pink{\bf \longrightarrow Perimeter _{(Rectangular) } = 2( Length + Breadth) }\)

\(\qquad\)\( \sf \longrightarrow Perimeter _{(Rectangular) }= 2( 11.5 +8) \)

\(\qquad\)\( \sf \longrightarrow Perimeter _{(Rectangular) } = 2 \times 19.5\)

\(\qquad\)\(\pink{ \bf \longrightarrow Perimeter _{(Rectangular) } = 39\: mm}\)

_______________________________________

Answer:

Step-by-step explanation:

In this question we are given with ,

And we're asked to find the perimeter of rectangle .

Solution : -

We know that ,

\( \pink{ \boxed{\sf{Area \: of \: rectangle = L × W}}}\)

Where ,

So from this formula we can find the width of rectangle and equating it with 92 ( because 92 is the given area ) . Substituting value of length :

\( \longmapsto \: 11.5 \times W = 92\)

Step 1 : Multiplying 11.5 and W :

\( \longmapsto \: 11.5W = 92\)

Step 2 : Dividing by 11.5 on both side :

\( \longmapsto \: \frac{ \cancel{11.5}W}{ \cancel{ 11.5}} = \frac{92}{11.5} \)

On further calculations we get :

\( \longmapsto \: W = \cancel{\frac{920}{115} }\)

Step 3 : By cancelling 920 by 115 we get :

\( \longmapsto \: \purple{\boxed{ \bold{W = 8 \: mm}}}\)

We know that ,

\( \blue{ \boxed{ \sf{Perimeter \: of \: rectangle = 2 ( L +W )}}}\)

Where ,

Substituting values in formula :

\( \longrightarrow \: 2(11.5 + 8)\)

Step 1 : Solving parenthesis :

\( \longrightarrow \: 2(19.5)\)

Step 2 : Multiplying 2 with 19.5 :

\( \longrightarrow \: \green{\boxed{ \bold{39 \: mm}}}\)

The factorized form for the given polynomials are:

8. 5n(3n² - 4).

10. x²(x - 8).

11. 4x(2x² - 3x + 10).

12. 6x³(1 + 5x).

13. 2w(w² + 3w - 18).

14. 3c²(4c - 1).

15. 2x(x + 3 - 80).

In the question, we are asked to factor the given polynomials.

8. 15n³ - 20n.

The given polynomial is 15n³ - 20n.

The terms are 15n³ and - 20n.

The HCF of the terms is 5n.

Taking the HCF common in the given polynomial, we get 5n(3n² - 4), which is the required form.

Going by the same method, the errors will have a solution as:-

10. x³ - 8x².

The factorized form is x²(x - 8).

11. 8x³ - 12x² + 40x.

Factorized form is 4x(2x² - 3x + 10).

12. 6x³ + 30x⁴.

The factorized form is 6x³(1 + 5x).

13. 2w³ + 6w² - 36w.

The factorized form is 2w(w² + 3w - 18).

14. 12c³ - 3c².

The factorized form is 3c²(4c - 1).

15. 2x² + 6x - 80.

The factorized form is 2x(x + 3 - 80).

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Answer:

steeper

Step-by-step explanation:

y = mx + c where m is the slope and c is the y-intercept.

The slope has been changed from 2 to 4. The higher the slope, the steeper it is. Thus, the slope is steeper now.

Answer:

i'm not sure sorry

Step-by-step explanation:

Answer:

5/2 or 2.5

Step-by-step explanation:

Divide both sides by 2.

The polynomial expression that represents the perimeter is (3x^3 +3x -148)ft and the value is 182ft

Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable.

Perimeter of the triangle is the sum of the sides of the triangle which is = 2x^2 -120 + x^2 -5x +8x -28

Perimeter = (3x^2 +3x -148)ft

when x = 10

Perimeter = 3(10)^2 +3(10) -148 = 182ft

In conclusion the expression  (3x^2 +3x -148)ft is the expression for the perimeter of the triangle and the value is 182ft

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Answer: L = 3/4

Option A. The Root Test says that the series converges absolutely.

Step-by-step explanation:

By using the root test equation given in the question. L = 3/4

Since L < 1, the series converges absolutely.

For clarity of expression, the detailed calculation is contained in the attached file. Check the file attached for the complete calculation to this question.

Step-by-step explanation:

Answer:

sin(100°) = 0.985

sin(-100°) = -0.985

Step-by-step explanation:

In a unit circle, each point (x, y) on the circumference corresponds to the coordinates (cos θ, sin θ), where θ represents the angle formed between the positive x-axis and the line segment connecting the origin to the point (x, y).

Therefore, sin(100°) equals the y-coordinate of the point (-0.174, 0.985), so:

\(\boxed{\sin(100^{\circ}) = 0.985}\)

Similarly, sin(-100°) equals the y-coordinate of the point (-0.174, -0.985), so:

\(\boxed{\sin(-100^{\circ}) = -0.985}\)

In the unit circle the value of sin (100) = 0.985 and the value of sin (-100) = -0.985, in three decimal places.

The value of the sine of the angles is calculated by applying the following formula as follows;

The value of sin (100) is calculated as follows;

sin(100°) corresponds to the y-coordinate of the point (-0.174, 0.985) as given on the coordinates of the unit circle.

sin (100) = 0.985

The value of sin (-100) is calculated as follows;

sin(100°) corresponds to the y-coordinate of the point (-0.174, -0.985), as given on the coordinates of the circle.

sin (-100) = -0.985

Thus, in the unit circle the value of sin (100) = 0.985 and the value of sin (-100) = -0.985, in three decimal places.

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The simplified expression for x+2x-8+3x+1-2x is 4x - 4.

Expression is a term used to describe a wide variety of communication methods such as verbal, nonverbal, written, and artistic. It is the way we communicate our thoughts, feelings, and ideas to others. It is an important part of our lives, from the simplest forms of communication like body language to more complex forms like written literature. Expression is a powerful tool for self-expression, communication, and connection.

The expression x+2x-8+3x+1-2x can be simplified by combining like terms.

First, the x-terms can be combined, resulting in 4x:
x + 2x + 3x - 2x = 4x

Next, the remaining constants can be combined, resulting in -4:
4x - 8 + 1 = -4

Finally, the resulting expression can be written as 4x - 4.

Therefore, the simplified expression for x+2x-8+3x+1-2x is 4x - 4.

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Answer:

(-7) (-10x - 3y = -18)

(10) (-7x - 8x = 11)

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

70x + 21y = 126

+ -70 - 80x = 110

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

-59x = 236

x = -4

Answer

\( \huge{ \boxed{ \text{(3 \:, - 4)}}}\)

✑ \( \underline{ \underline{ \text{First ,\: let's \: know \: about \: elimination \: method}}}\) :

☇ In this method , we add or subtract the given equations to eliminate one of the two variables by making their coefficients equal. Then , a single equation with one variable so obtained is solved to find the value of the variable. The value of the variable is substituted to any one equation to find the value of the eliminated variable.

☯ \( \underline{ \underline{ \text{Let's \: solve}}} : \)

\( \underline{ \text{Original \: system}} : \)

\( \text{ - 10x - 3y = - 18 - - - - Equation\: (i)}\)

\( \text{ - 7x - 8y = 11 - - - - Equation \: (ii)}\)

\( \text{Step \: 1} : \) Take L.C.M ( Lowest Common Multiple ) of 10 and 7. For this , find the prime factors of each number. Then, take out the common prime factors and other remaining prime factors and multiply them.

L.C.M = Common factors × Remaining Factors

= 1 × 2 × 5 × 7

= 70

\( \text{Step \: 2} : \) Multiply equation ( i ) by 7

\( \text{7( - 10x - 3y ) = - 18  * 7}\)

⇢ \( \text{ - 70x - 21y = - 126 - - - - equation \: (iii)}\)

\( \text{Step \: 3} : \)Multiply equation ( ii ) by 10

\( \text{10( - 7x - 8y) = 11 \: * \: 10}\)

⇢ \( \text{ - 70x - 80y = 110 - - - - equation \: (iv)}\)

\( \text{Step \: 4} : \) Subtract equation ( iv ) from equation ( iii ) :

Also Remember that while subtracting , sign of each term of the second equation changes. Here , we are eliminating x . So to make the coefficient of y same , equation ( i ) is multiplied by 7 and equation ( ii ) is multiplied by 10.⇩

\( \text{ - 70x - 21y = - 126}\)

\(\text{+70x + 80y = - 110}\)

___________________

\( \text{ \: \: \: \: \: \: 59y = - 236}\)

Solve :

⇢ \( \text{59y/59 = - 236/59}\)

⇢ \( \boxed{ \bold{ \text{y = - 4}}}\)

\( \text{Step \: 5} : \)

Substitute the value of y into equation ( iii ) , we get :

\( \text{ - 70x - 21y = - 126}\)

➳ \( \text{ - 70x - 21( - 4) = - 126} \)

➳ \( \text{ - 70x - ( - 84) = - 126} \)

➳ \( \text{ - 70x + 84 = - 126}\)

➳ \( \text{ - 70x = - 126 - 84}\)

➳ \( \text{ - 70x = - 210}\)

➳ \( \text{ - 70x/  - 70 = - 210/  - 70}\)

➳ \( \boxed{ \bold{ \text{x = 3}}}\)

\( \bold{ \underline{ \text{Hence ,\: x = 3 \: and \: y = - 4}}}\)

Hope I helped!

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~ \( \sf{TheAnimeGirl} \) ♪

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The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is given as follows:

0.5874 = 58.74%.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The parameters for this problem are given as follows:

\(\mu = 17.2, \sigma = 2.5, n = 40, s = \frac{2.5}{\sqrt{40}} = 0.3953\)

The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is the p-value of Z when X = 18.1 subtracted by the p-value of Z when X = 17.1, hence:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem:

\(Z = \frac{X - \mu}{s}\)

Z = (18.1 - 17.2)/0.3953

Z = 2.28

Z = 2.28 has a p-value of 0.9887.

Z = (17.1 - 17.2)/0.3953

Z = -0.25

Z = -0.25 has a p-value of 0.4013.

Hence:

0.9887 - 0.4013 = 0.5874 = 58.74%.

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The half life of the iodine is obtained as 6.2 s.

Let us recall that the half  life would be the time that is taken for about half of the original radioactive isotope that remains in the sample, to become depleted in the thyroid treatment.

Given that we have the fact that the decay constant that we have in the process is given as 0.1113 in the question and we know that;

Half life = 0.693/K

Half life = 0.693/0.1113

Half life = 6.2 s

It would have the half life about 6.2 s.

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Answer:

12-17

Step-by-step explanation:

this is right. trust (:

Step-by-step explanation:

Simple, she found the sum of the interior angles not exterior angles.

The exterior angles of any polygon add up to 360 degrees.

What Cindy did was found the total interior angle measure of a hexagon which is 720

Answer:

\(q=45\)

Step-by-step explanation:

Notice that \((q+2)^{\circ}\) and \((3q-2)^{\circ}\) form a linear pair, that is, they sum to \(180^{\circ}\) as follows:

\((q+2)^{\circ}+(3q-2)^{\circ}=180^{\circ}\\(q+2+3q-2)^{\circ}=180^{\circ}\\(4q)^{\circ}=180^{\circ}\\4q=180\\q=\frac{180}{4}\\q=45\)