Solve for x.



6(x - 2) = 4

(a) 40 unit have to be the number of units sold that will yield maximum revenue.

(b) The price per unit that will yield maximum revenue, will be $1.195.

(a) We have to find the number of units sold that will yield maximum revenue

Given demand function is

D(x)=130e^{-0.025x}

where is the number of units sold each week

Revenue function R(x) = xD(x)

R(x) = x∙130e^{-0.025x}

To find maximum revenue put,

R’(x) = 0

⇒d/dx(x∙130e^{-0.025x}) = 0

⇒130 d/dx(x∙e^{-0.025x}) = 0

⇒130[e^{-0.025x}+xe^{-0.025x} ∙(-0.025x)]=0

⇒130e^{-0.025x} ∙(1-0.025x)=0

⇒1 - 0.025x=0

⇒0.025x = 1

⇒x = 1/0.025

⇒x = 40units

R''(x) = 130d/d[x(e^{-0.025x}-0.025xe^{-0.025x} )]

R''(x) = 130[-0.025e^{-0.025x}-0.025e^{-0.025x}+0.00625xe^{-0.025x}]

R''(x)|x=40 = 130-0.025*40[0.050+0.00625*40]

R''(x)|x=40 = 130/e ∙(-0.025)

R''(x)|x=40 = (130*(-0.025))/e < 0

At x= 40 units, the revenue will maximize.

$0 units will yield maximum revenue.

(2) Now we have to find the price per unit that will yield maximum revenue.

D(x) = 130e-0.025x

D(40) = 130e^{-0.025*40}

D(40) = 130e^{-1}

D(40) = 130/e

D(40) = 47.82(in dollar)

Price per unit = d(40)/40

Price per unit = 47.82/40

Price per unit = $1.195

The price per unit that will yield maximum revenue, will be $1.195.

To learn more about to maximum revenue link is here

brainly.com/question/1332812

#SPJ4

The exponential function sketched is defined as follows:

y = 2(0.5)^x - 6.

The standard definition of an exponential function is given as follows:

y = a(b)^x + c.

In which:

From the graph, the horizontal asymptote is of y = -6, hence the parameter c is given as follows:

c = -6.

When x = 0, y = -4, hence the parameter a is given as follows:

-4 = a - 6

a = 2.

Hence:

y = 2(b)^x - 6.

When x = -1, y = -2, hence the parameter b is given as follows:

2(b)^(-1) - 6 = -2

2/b = 4

b = 0.5.

Hence the function is of:

y = 2(0.5)^x - 6.

More can be learned about exponential functions at https://brainly.com/question/30113628

#SPJ1

\(\begin{align}\sf\:\Phi_1 &= \iint_{S_1} (-2u^6\cos(v) - 2u^3\sin(v)) \, du \, dv \\ &= \int_{0}^{1} \int_{0}^{2\pi} (-2u^6\cos(v) - 2u^3\sin(v)) \, dv \, du \end{align} \\\)

Answer:

-24

Step-by-step explanation:

The standard from of equation of a line is expressed as g(x) = mx+c where;

m is the slope

c is the y-intercept of the line.

Given the expression g(x)= (- 8)(x +3), rewriting in standard form first we have;

g(x)= (- 8)(x +3)

gx)= -8x - 24

On Comparing with g(x) mx+ c, we will see that;

c = -24

Hence the y-intercept of the quadratic function is -24

Answer:

\(\textsf{1.(a)} \quad x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

\(\textsf{1.(b)} \quad 9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\begin{aligned}\textsf{2.(a)}\quad3x^2-24x+48&=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\\&=3\left(x-\boxed{4}\right)^2\end{aligned}\)

\(\begin{aligned}\textsf{2.(b)}\quad \dfrac{1}{2}x^2+8x+32&=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\\&=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\end{aligned}\)

Step-by-step explanation:

(a) When completing the square for a quadratic equation in the form ax² + bx + c where the leading coefficient is one, we need to add the square of half the coefficient of the x-term:

\(x^2-14x+\left(\dfrac{-14}{2}\right)^2\)

\(x^2-14x+\left(-7\right)^2\)

\(x^2-14x+49\)

We have now created a perfect square trinomial in the form a² - 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Therefore:

\(a^2=x^2 \implies a=1\)

\(b^2=49=7^2\implies b = 7\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

(b) When completing the square for a quadratic equation where the leading coefficient is not one, we need to add the square of the coefficient of the x-term once it is halved and divided by the leading coefficient, and then multiply it by the leading coefficient:

\(9x^2 + 30x +9\left(\dfrac{30}{2 \cdot 9}\right)^2\)

\(9x^2 + 30x +9\left(\dfrac{5}{3}\right)^2\)

\(9x^2 + 30x +9 \cdot \dfrac{25}{9}\)

\(9x^2 + 30x +25\)

We have now created a perfect square trinomial in the form a² + 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 +2ab + b^2 = (a +b)^2}\)

Therefore:

\(a^2=9x^2 = (3x)^2 \implies a = 3x\)

\(b^2=25 = 5^2 \implies b = 5\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\hrulefill\)

(a) Factor out the leading coefficient 3 from the given expression:

\(3x^2-24x+48=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\)

We have now created a perfect square trinomial in the form a² - 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=3\left(x-\boxed{4}\right)^2\)

(a) Factor out the leading coefficient 1/2 from the given expression:

\(\dfrac{1}{2}x^2+8x+32=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\)

We have now created a perfect square trinomial in the form a² + 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2+2ab + b^2 = (a +b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\)

Step-by-step explanation:

Since ABCD is a rectangle

⇒ AB = CD and BC = AD

x + y = 30 …………….. (i)

x – y = 14 ……………. (ii)

(i) + (ii) ⇒ 2x = 44

⇒ x = 22

Plug in x = 22 in (i)

⇒ 22 + y = 30

⇒ y = 8

75 units are the value of x.

If PAB is a secant to a circle intersecting it at A and B and PT is a tangent then PA.PB = PT².

In the given case,

PA  = 48

PT = 60

PB = x

Thus,

60² = 48*x

x = 3600/48

x = 75

Therefore, the value of x is 75 units.

Learn more about secant here:

https://brainly.com/question/23026602

#SPJ1

Answer:

a) the probability that the next ream out- lasts the present one by more than 2 days is 0.0787

b) the number of reams that must be purchased is 19

Step-by-step explanation:

Given the data in the question;

Lets X₁ and X₂ be the two random variables that represents the first and second ream lasts

given that both random variables follow normal distribution with mean 4 and standard deviation 1.

a)

Find the probability that the next ream out- lasts the present one by more than 2 days.

P( X₂  - X₁ > 2 ) = P( [(X₂  - X₁ - E(X₂  - X₁)) / √(V(X₂  - X₁)] > [ (2-E(X₂  - X₁))/√(V(X₂  - X₁) ]

= 1 - P( Z ≤ [2-(μ₂  - μ₁)] / [√( V(X₂) + V(X₁) ) ] )

= 1 - P( Z ≤ [2-(4  - 4)] / [√( 1 + 1 )] )

= 1 - P = ( Z ≤ 2 / √2 )

= 1 - p( Z ≤ 1.4142 )

from excel; p( Z ≤ 1.41 ) = 0.9213

P( X₂  - X₁ > 2 ) = 1 - 0.9213

P( X₂  - X₁ > 2 ) = 0.0787

Therefore, the probability that the next ream out- lasts the present one by more than 2 days is 0.0787

b)

How many reams must be purchased if they are to last at least 60 days with probability at least 80%

total value is 4n

standard deviation is nσ

so

P(nX ≥ 60 ) = 0.80

P( nX-nμ /nσ  ≥  60-nμ/nσ) = 0.80

P( Z ≥  60-4n/n) = 0.80

1 - P( Z ≥  60-4n/n) = 0.80

P( Z < z ) = 0.20

now since z = 60-4n/n

from standard normal table

critical value of z corresponding to cumulative area of 0.20 is -0.841

so

z = - 0.841

60-4n/n =  -0.841

60 - 4n =  -0.841n

60 = -0.841n + 4n

60 = 3.159n

n = 60 / 3.159

n = 18.99 ≈ 19

Therefore, the number of reams that must be purchased is 19

Answer:

22222

Step-by-step explanation:

Answer:

16.7 would be the bigger

Step-by-step explanation:

Hope this helps :)

Sorry if im wrong :(

Answer:

16.7 is bigger than 1.67.

Step-by-step explanation:

Numbers have a structure, and a part of that is places. (ex. tens place, one's place, hundreds place, etc.) If you look at the numbers above, only one has a tens place. (Think about it this way; you're comparing 0 to 1 for the tens place. 1 is a larger number, so the number containing 1 in the tens place is larger) Therefore, 16.7 is larger than 1.67

Answer:

2.6 x 0.47 = 1.222

Step-by-step explanation:

Answer: (0.79, 3.05 )

Step-by-step explanation:

Confidence interval for the population mean:

\(\overline{x}\pm z^c\dfrac{\sigma}{\sqrt{n}}\)

, where \(\overline{x}\) = Sample mean

\(\sigma\) = population standard deviation

n= sample size.

\(z^c\) = Critical z value for confidence interval c.

As per given:

n= 10

\(\overline{x}=1.92\)

\(\sigma=1.83\)

Critical z-value for 95% confidence = 1.96

A 95% confidence interval for the mean opinion in the population of all licensed drivers:-

\(1.92\pm (1.96)\dfrac{1.83}{\sqrt{10}}\\\\=1.92\pm1.134\\\\= (1.92-1.134,\ 1.92+1.134)\\\\\approx(0.79,\ 3.05 )\)

Hence, a 95% confidence interval for the mean opinion in the population of all licensed drivers = (0.79, 3.05)

Answer:

No, the Normal/large sample condition is not met. A confidence interval assumes that the underlying population follows a normal distribution and that the sample size should be at least 30. Since the sample size in this case is only 10, the Normal/Large Sample condition is not met and the conditions for constructing a confidence interval are not met.

y - incercept = 371.4

The linear relationship illustrated in the provided table can be effectively described by the equation Y = -4x + 2. Option D.

To determine the equation that represents the given table with the values of x and y, we can observe the pattern and find the equation of the line that fits these points.

Given the table:

X: 2 0 4

Y: -4 3 1

We can plot these points on a graph and see that they form a straight line.

Plotting the points (2, -4), (0, 3), and (4, 1), we can see that they lie on a line that has a negative slope.

Based on the given options, we can now evaluate each equation to see which one represents the line:

Y = 1/2x + 5

When we substitute the x-values from the table into this equation, we get the following corresponding y-values: -3, 5, and 6. These values do not match the given table, so this equation does not represent the table.

Y = -1/2x + 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: 4, 3, and 2. These values also do not match the given table, so this equation does not represent the table.

Y = 2x - 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -4, -3, and 5. These values do not match the given table, so this equation does not represent the table.

Y = -4x + 2

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -6, 2, and -14. Interestingly, these values match the y-values in the given table. Therefore, the equation Y = -4x + 2 represents the table.

In conclusion, the equation Y = -4x + 2 represents the linear relationship described by the given table. So Option D is correct.

For more question on equation visit:

https://brainly.com/question/29174899

#SPJ8

Answer:

Answere is X= 8

Step-by-step explanation:

Use sine law

Sin(angle) = Opposite/ Hypotenuse

Sin (30) = 4 /X

X = 4 / sin (30)

X = 8

Answer:

  C. RP = 4.5

Step-by-step explanation:

You want to know what condition is sufficient to show ∆ABC ~ ∆QPR, given  three sides and 2 angles in ∆ABC, and 2 sides in ∆QPR.

Similarity can be shown if all three sides are proportional, or if two angles are congruent.

The offered answer choices only list one angle, so none of those will work. The answer choice that makes the third side of ∆QPR be in the same proportion as the corresponding side of ∆ABC is the condition of interest.

  C. RP = 4.5

__

Additional comment

The side ratios in the two triangles are ...

  AB : BC : CA = 10 : 9 : 6

  QP : PR : RQ = 5 : PR : 3

For these ratios to be the same, PR must be half of BC, just as the other segments in ∆QPR are half their counterparts in ∆ABC.

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the representation of the chicken wings

Let the chicken wing be represented by x

STEP 2: Equate the two amounts

Since they both spent same amount of money, this means that;

STEP 3: Solve for x

Hence, each chicken wing costs $0.75

Answer: i believe the answer is B

Step-by-step explanation: because if p to q is true, then that means p and q are both true!

In the first column, 20.53 kilometer is most precise

In second column the scale that measures 1/10 of a kg is most precise.

In third column, 3.72 millimeters is precise.

For 20.53 kilometer, there are two digits after the decimal point. So, the measurement measures even the slightest change in decimals of the measurement.

1/10 of a kg can be written as 0.1 kg. So, in this scale the weight is measured upto the smallest change of one decimal point. For the scale that measures the nearest kg, the small change is not measured as there are no digits after decimal in the measurement. For example, compare the weights 500 kg and 500.5 kg . 500.5 kg is measured in 1/10 of a kg scale. The extra 0.5 kg s measure is shown. So, it will be a more precise value.

In 3.72 millimeters, there are two digits after the decimal point. So, when a measurement is taken, we get a precision upto two decimal places, while for 3.7mm, the measurement can be taken only upto one decimal place and for 3 mm no decimal points are there.

Answer:

c) 13%

Step-by-step explanation:

Given information,

→ The cost of a jacket increased from the price $75.00 to $84.75.

Now we have to,

→ find the % increase of cost of jacket.

Let's solve the problem,

→ ((84.75 - 75)/75) × 100

→ (9.75/75) × 100

→ 0.13 × 100

→ 13%

Hence, the answer is 13%.

The following weights (in pounds) are within 1.5 units of the standard deviation of the mean:

A. 4.4

B. 4.6

D. 5.2

E. 6.9

F. 7.6

The mean weight of the chickens in this population is 6.3 pounds, and the standard deviation is 1.2 pounds. To be within 1.5 units of the standard deviation, we need to look at the range of weights that are 1.2 +/- 1.5, which is 4.7 to 7.9 pounds.

This means that the weights within this range are 4.4, 4.6, 5.2, 6.9, 7.6, and any other weights that fall within the range. Therefore, the weights within 1.5 units of the standard deviation of the mean are:

A. 4.4, B. 4.6, D. 5.2, E. 6.9, and F. 7.6.

The standard deviation measures the spread of the data from the mean. In this case, the mean is 6.3 pounds and the standard deviation is 1.2 pounds. This means that the data points on either side of the mean will be 1.2 pounds away from it.

To learn more about standard deviation of the mean, use the link:

brainly.com/question/16030790

#SPJ4

Answer:

50.50$

Step-by-step explanation:

8.5x+25

x is the hours

8.5(3)+25= 50.50

The measure of angle x on the straight line is 130 degrees.

The sum of interior angles in a triangle equals 180 degrees.

To determine the value of x, we first determine its suplemetary angle x .

Hence:

40 + 90 + ( suplemetary angle of x ) = 180

Solve for the suplementary angle:

130 + ( suplemetary angle of x ) = 180

Suplementary angle of x = 180 - 130

Suplemetary angle of x = 50 degree

Now, we can find the measure of  angle x.

Note that, sum of angles on a straight line equals 180 degree.

Hence:

x + ( suplemetary angle of x )  = 180

x + 50 = 180

Solve for x

x = 180 - 50

x = 130 degrees.

Therefore, the value of x is 130 degrees.

Learn about area of triangle here: brainly.com/question/29156501

#SPJ1

Answer: 38.8

Step-by-step explanation:

Step-by-step explanation:

Calculate with Parenthesis ( \(7*5\))

\(7*5=35\)

\(35*3\)÷3+6

Multiply and divide ( left to Right)

35*10/3

=350/3

350/3+6

Add and subtract (left to right):

350/3+6

=368/3

Convert improper fraction to mixed numbers:

368/3=122

Answer:

368/3=\(122 \frac{2}{3}\)

Answer:

An arithmetic sequence with a common difference of −2 is 20,18,16,14,12..

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is same. Here, the common difference is -2, which means that each term in the sequence is obtained by subtracting 2 from the previous term.

To find the arithmetic sequence with a common difference of -2, you can start with an first term and then subtract 2 successively to find the subsequent terms.

Let the initial term is 20. Subtracting 2 from 20, we get 18. Subtracting 2 from 18, we get 16. Continuing this pattern, we subtract 2 from each subsequent term to generate the sequence. The arithmetic sequence with a common difference of -2 starting from 20 is

20,18,16,14,12

In this sequence, each term is obtained by subtracting 2 from the previous term, resulting in a common difference of -2.

There are two types of errors that could be made:

a Type I error and a Type II error.

We have,

In step 5 of the hypothesis test, we make a decision to either reject or fail to reject the null hypothesis.

If we reject the null hypothesis, there are two types of errors that could be made:

a Type I error and a Type II error.

A Type I error occurs when we reject a true null hypothesis.

In this context, it means that we conclude that the percentage of packages delivered late is greater than 13% when in reality it is not.

This error is also known as a false positive.

A Type II error occurs when we fail to reject a false null hypothesis.

In this context, it means that we conclude that the percentage of packages delivered late is less than or equal to 13% when in reality it is greater than 13%. This error is also known as a false negative.

The probability of making a Type I error is denoted by α, which is given in the problem statement as α = 0.01.

Therefore, if we reject the null hypothesis, there is a 1% chance that we are making a Type I error.

Thus,

The probability of making a Type II error depends on the effect size, sample size, and significance level of the test.

Learn more about hypothesis testing here:

https://brainly.com/question/30588452

#SPJ1