The first three terms of an arithmetic sequence are x, 2x + 4, 5x. Find the value of x.

It is to be noted that at the equilibrium level, the Equilibrium price/output combination is $4 and 300,000 units respectively. See further calculations and answer below.

Recall that the equilibrium level of the national income is defined as that point where the aggregate supply  (QS) and the aggregate demand (AQD) are the same.

To calculate the market equilibrium price/output combination (EQL:

Step I - Recall the given data

Recall that at EQL, QD = QS

Where:

Qd = 500000 – 50000P; and ....................1

Qs = -100000 + 100000P. ...........................2

Hence, at EQL,

500000 – 50000P = -100000 + 100000P

⇒ 150,000P = 600,000 [divide both sides by 150,000

⇒ P = 600,000/150,000

⇒P = $4

Step II

To get Q, substitute P into (1)

thus, we have:

500,000 – 50000 (4)

500,000 – 200,000

= 300,000 units.

Hence, at EQL, P = $4 and Q = 300,000 units.

B)i What is P = $3?

Recall Step II above,

Simply substitute $3 into  (1)

⇒ 500,000 – 50,000 (3)

= 500,000 – 150,000

= 350,000 units

ii) what is P = $6, just repeat the above steps to get

200,000 units.

C) Price Elasticity of Demand (PED) at Equilibrium Price

The PED is the percentage change in the quantity requested as a result of a 1% change in price. The PED coefficient is often negative, although economists frequently overlook the sign. If the PED coefficient is less than one, demand for an item is generally inelastic (in absolute value).

The formula for demand (PED) at P = 6 is determined using the formula:

PED = %Δ in QD / %Δ in Price..................1

%Δ in QD = (200,000-300,000)/300,000 ..............2

With 300,000 beings (Original Unit at Equilibrium)

Hence %Δ in QD = -0.333

%Δ in Price =  (6-4)/4

= 1/2j or 0.5

PED = -0.333/0.5

PED = |-0.666|

Given that the PED is < 1, we can conclude that the demand for dry cleaning is inelastic.

In a situation where it is greater than 1, then the demand is elastic.

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Using the substitution method, if sum of two numbers is 96 and difference of the two numbers is 42, then the two numbers are 69 and 27

Consider the largest number as x and the smallest number as y

The sum of two numbers is 96

The equation will be

x+y = 96

x = 96-y

The difference of the two numbers 42

x-y = 42

Use the substitution method here

Substitute the value of x in the second equation

x-y =42

(96-y)-y =42

96-2y = 42

-2y = 42-96

-2y = -54

y = 27

Substitute the value of y in the first equation

x+y = 96

x+27 = 96

x = 96-27

x = 69

Hence, using the substitution method, if sum of two numbers is 96 and difference of the two numbers is 42, then the two numbers are 69 and 27

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Answer:30

Step-by-step explanation:

Answer:

[tex]2x^2+23x-10[/tex]

Step-by-step explanation:

1) distribute the parenthesis by multiplying 5 into (x^2 - 2) and -3x into (x - 7)

[tex]5x^2-10 +2x-3x^2+21x\\[/tex]

2) simplify by adding and subtracting like terms

[tex]2x^2+23x-10[/tex]

The solutions for the trigonometric cosine equation are [0, 90,2pi].

What is trigonometric cosine function?

Trigonometric is one of the branch in mathematics which is used to study the relationship between the length and angles. Its angle is categorized into six form depending upon their sides.

To calculate the solution of the given equation in the interval of [0, 2 pi].

Therefore, the given equation in the form of the trigonometric function is as written below:

[tex]cos^{2} 0 - 2cos0 +1 = 0\\(cos0-1)^{2} =0[/tex]

Hence, the solutions for the trigonometric cosine equation are [0, 90,2pi].

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Answer: C=D\A-B THAT IS THE ANSWER

Step-by-step explanation:

The sample can be 25% of the workers of the company and 50% of the retirees.

Sampling is the practice of selecting a small group of individuals (a statistical sample) from a statistical population in order to make an educated guess about the characteristics of the full population.

Now of the given options sample can only be selected from the groups that directly affect the president of the company.

Therefore the options will be :

25% of the workers at the company

50% of the retirees from the company

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x − 8 =  − 10

Explanation: 9x −13 = − 31 Add 13 to each side.

Answer:

-1

Step-by-step explanation:

3x = 21

Divide both sides by the co efficient of x

3x = 21

3      3

x = 21/3

x = 7

Find x - 8

x = 7

7 - 8

= -1

The new mean is 18.4

According to the question,

The mean of 20 observations is 17

So the total value of all the observations = 20*17

= 340

The new value will be = 340 +40-12

= 368

Then,

The new mean of 20 observations will be= 368÷20

= 18.4

Hence, the new mean is 18.4

Mean is the average of a set of two or more numbers. It is of two types; arithmetic mean and geometric mean. It is part of statistics.

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The question provides that an initial fee of $1000 and a monthly fee of $115 is paid.

Since the initial fee is a one-time payment and the monthly fee is a recurring payment, over x months, the fee that would have been paid is given o be:

After 1 year, 12months would have passed. This means that we can scalculate the cost using x = 12 in the equation:

ANSERS

(a) The function is:

(b) At the end of one year, he would have paid $2,380.

Differentiation of the given function f(x)=sinx/(1+tanx)​ is equal to

(cos³x -sin³x) / (cos²x)(1 + tanx)².

As given in the question,

Given function : f(x) = sinx /(1 + tanx )

Let u = sinx , v = ( 1 + tanx)

Differentiate the given function with respect to x

du/dx = cosx

dv/dx = sec²x

         = 1/cos²x

(d/dx)(f(x)) = (d/dx)(sinx /(1 + tanx ))

                = ( d/dx) (u / v)

                = [v (du/dx) -u (dv/dx)] / (v)²

               = [(1+tanx)(cosx) -(sinx)(1/cos²x)] / (1 + tanx)²

               = [cos²x(cosx + sinx) -sinx]/ (cos²x)(1 + tanx)²

               = [cos³x +sinx(cos²x -1)] / (cos²x)(1 + tanx)²

               =  (cos³x -sin³x) / (cos²x)(1 + tanx)²

Therefore, differentiation of the given function f(x)=sinx/(1+tanx)​ is equal to

(cos³x -sin³x) / (cos²x)(1 + tanx)².

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The area, A, of the regular polygons found their side lengths, s and the length of their apothem, are;

4. A ≈ 2144.5 cm²

6. A = 12080 in²

8. A ≈ 1168.5 m²

A regular polygon is a polygon that have sides of the same length and that the sides are symmetric about a common central point.

The area of a regular polygon is given by the formula;

[tex] \displaystyle{A = \frac{n \times s\times a}{2} }[/tex]

Therefore, we have;

4. The area of a regular pentagon is given by the formula;

[tex]\displaystyle{A = \frac{5 \times s\times a}{2} }[/tex]

Where;

a = 24.3 cm, s = 35.3 cm, we have;

[tex]\displaystyle{A = \frac{5 \times 35.3 \times 24.3}{2} \approx 2144.5}[/tex]

6. The area of a regular octagon is given by the formula;

[tex]\displaystyle{A = \frac{8 \cdot s\cdot a}{2} }[/tex]

Where;

a = 60.4 in,

s = 50 in

Which gives;

[tex]\displaystyle{A = \frac{8 \times 50\times 60.4}{2} = 12080 }[/tex]

8. The area of a regular decagon is given by the formula;

[tex]\displaystyle{A = \frac{10 \times s\times a}{2} }[/tex]

Where;

a = 19 m

s = 12.3 m

Which gives;

[tex]\displaystyle{A = \frac{10 \times 12.3\times 19}{2} = 1168.5}[/tex]

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Supposing that the two points are (2,4) and (10,10), the distance between them is given by:

A. 10.

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, with the hypotenuse being the distance between them.

For this problem, the two points are (2,4) and (10,10), hence the distance between them is given as follows:

[tex]D = \sqrt{(10 - 2)^2+(10 - 4)^2} = \sqrt{100} = 10[/tex]

Hence the distance is of 10 units and option A is correct.

This problem is incomplete, and I could not find it on any search engine, hence we are going to suppose that the two points are (2,4) and (10,10).

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The perimeter in feet of a rectangle with height 4 1/6 feet and width 3 1/3 is 15 feet.

It should be noted that the perimeter of a rectangle is calculated thus:

Perimeter = 2(Length + Width).

Based on the information, the following can be deduced:

Length = 4 1/6 feet

Width = 3 1/3 feet

Perimeter = 2(Length + Width).

Perimeter = 2(4 1/6 + 3 1/3)

Perimeter = 2(7 1/2)

Perimeter = 15 feet

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The value of the expression one fifth times the quantity 3 times x plus 10 end quantity minus 11 over 15 times x is 2 - 2/15x.

It should be noted that expressions are simply used to show the relationship that exists between the variables that are given.

In this case, one fifth times the quantity 3 times x plus 10 end quantity minus 11 over 15 times x will be illustrated as:

= 1/5(3x + 10) - (11/15x)

= 3/5x + 2 - 11/15x

= 9/15x + 2 - 11/15x

= 2 - 2/15x

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Answer: straight line that makes the right angle (90 degrees) with the other

Step-by-step explanation: In other words, if two lines intersect each other at the right angle, then the lines are perpendicular to each other

The probability that the aircraft is overloaded is 97.98%, which means the pilot should take the action.

In a Normal distribution with mean ц and standard deviation σ, the z-score of a measure x is given by:

Z = X-ц / σ

· It measures how many standard deviations the measure is from the mean.

· After finding Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

· By the Central Limit Theorem, the sampling distribution of sample means of the size n has standard deviation σ

σ = σ / [tex]\sqrt{n}[/tex]    

σ is standard deviation

n is the sample size.

Given that the mean and the standard deviation of the population is 176.1 lb and 35.4 respectively.

⇒ ц = 176.1  and σ = 35.4

For a sample of 43 passengers, we have

n = 43

σ =  [tex]\frac{35.4}{\sqrt{43}}[/tex]

σ = 5.398

Z = X-ц / σ

Z = [tex]\frac{165-176.1}{5.398}[/tex]

Z = -2.05 has p- value of 0.9798

The probability that the aircraft is loaded is

1 - p-value of Z

1 - 0.0202 = 0.9798

The probability that the aircraft is overloaded is 97.98%

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The sum of the angles on a straight line is 180 degrees. This means that

angle MJO + angle NJO = 180

From the information given,

angle MJO = 131

angle NJO = 15x + 4

Thus,

131 + 15x + 4 = 180

135 + 15x = 180

15x = 180 - 135 = 45

x = 45/15

x = 3

We would substitute x = 3 into angle NJO = 15x + 4

angle NJO = 15 * 3 + 4 = 45 + 4

angle NJO = 49

Answer:

The equation of the linear function represented in the table is y = -4x + 1.

Explanation:

Since the values in the x-variable are consecutive, let's take a look at the y-values.

Let's determine the common difference of the y-values.

As we can see, the common difference between the y-values is -4. Therefore, the slope of the equation is -4.

To determine the y-intercept, let's subtract -4 from -3 to determine the y-value at x = 0.

Hence, the y-intercept is 1.

Therefore, the equation is y = -4x + 1.

Answer:

Step-by-step explanation:

1.  5:3

2. 10:1

3. 7:1

4. 1:17

The coefficient of elasticity of demand would be equal to 2 .

The price elasticity of demand for a good determines how responsive the desired amount is to the price (PED).

We know that the coefficient of elasticity of demand is given by

ED = Change in demand(percent) ÷ change in price (percent)

ED = 20% ÷ 10% = 2

Hence the coefficient of elasticity of demand would be equal to 2 .

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1. The quotient of a number and six is five.

he algebraic expression ifor the previous sentence is:

x/6 = 5

multiply by 6 to solve for x:

x = 5(6)

x = 30

. Eight decreased by twice a number is four.

- 2x = 4 subtract 8 both sides

-2x = 4 - 8

2x = -4 divide by -2 both sides

x = 2

3. Three less than the division of a number to seven is one.

3 - x/7 = 1 subtract 3 both sidesa

-x/7 = 1 - 3

x/7 = -2 multiply by -7 both sides

x = 2

4. Seven times the difference of 15 and a number equals - 56.

7(15 - x) = -56 a

7(15) - 7x = -56

105 - 7x = -56 subtract 105 both sides

-7x = -56 - 105

7x = -161 divide by -7 both sides

x = 23

Answer:

A) $1.5

B)50 bars

Step-by-step explanation:

A) First find out how much money one bar costs: 18/12= 1.5

$1.5 is how much one costs

B) Now that you know how much one bar costs, divide 75 by 1.5 to determine how many bars you need to get to $75.

75/1.5=50

50 bars to get to $75

Answer:$1.50 per bar and she would have to sell 50 bars to get 75

Step-by-step explanation: brainliest please? i could really use it

Equation of the vertical line passing through point (-3, -5) is given by x = -3.

As given in the question,

Line passes through the point (-3, -5)

It represents the x- coordinate is equal to -3

And y- coordinate is equal to -5.

Condition for the line is given as vertical line.

Vertical line represent the value of x- coordinate remain constant.

It represent x-intercept

x = -3

x-intercept represents the equation of the vertical line.

Therefore, equation of the vertical line passing through point (-3, -5) is given by x = -3.

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The expected payback  is mathematically given as

$10

This is further explained below.

Generally, The formula for calculating the anticipated payback is the product of the likelihood times the value.

E(x) = p(x_1)*x_1 + p(x_2)*x_2 + .....

In this particular scenario, we have two distinct options for repayment.

winning

The payback is $2000-$10 = $1990

x_1 = 1990

The probability of winning is one out of 100 (since the choices are 0 to 99)

p(x_1) = 1/100

Losing

The payback is negative $8 since the individual did not win anything, which makes them lose.

x_2 = -10

Because there is only one number that can win, the other 99 numbers are considered to be losing numbers.

p(x_2) = 99/100

Therefore expected payback is

E(x) = p(x_1)*x_1 + p(x_2)*x_2

= (1/100)* 1990+ (99/100)*(-10)

= $10

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CQ

Find the expected payback for a game in which you bet $10 on any number from 0 to 999. If your number comes up, you get $2000

The expected payback is

The two lines never intersect (are parallel lines) thus the equation:

6 - x = 3 - x

Has no solutions.

Here we have the equation:

6 - x = 3 - x

And (supposedly) a graph of the two lines:

y = 6 - x

y = 3 - x

Notice that the part on the linear equations that depens of x is equal to the ones in the equation above.

So basically we have a system of equations:

y = 6 - x

y = 3 - x

Because "y" is the same thing in both equations, we can rewrite:

6 - x = y = 3 - x

If we remove the part in the middle, we return to the original equation:

6 - x = 3 - x

Now, the solution of that equation is given by the point where the two graphs of the linear equations intersect, it will never happen, because both linear equations are parallel (have the same slope) which means that the equation:

6 - x = 3 - x

Has no solutions.

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Answer:

its smthing about no solutions. Just pick the answer that says no solution satifies it

Step-by-step explanation:

i got it right on imagine math :))) (i dont have the screen shot)

We will see that there are 19,656,000 different passwords that can be made with the given characters.

We need to find the number of possible options for each character of the password.

The first character is a letter, so we have 26 options.

The second character is another letter, so we have 25 options (because we can't repeat).

Then we have 5 digits, for each digit we have 10 options (removing one for each subsequent one)

The total number of passwords is given by the product between the numbers of options.

P = 26*25*10*9*8*7*6 = 19,656,000

There are 19,656,000 different passwords that can be made.

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