Round 829.9 to the nearest whole number

Answer:

it's A

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Just got it correct

The given equation is a recursive formula where a subscript i equals the product of a subscript i-1 and 2, with the initial value of a subscript 1 being -4a.

The equation represents a recursive relationship between the terms of the sequence. Starting with the initial term, a subscript 1, the subsequent terms are determined by multiplying the previous term, a subscript i-1, by 2. This recursive formula can be written as a subscript i = a subscript i-1 * 2.

Given that a subscript 1 = -4a, we can use this initial value to find the subsequent terms of the sequence. To calculate a subscript 2, we substitute i = 2 into the formula:

a subscript 2 = a subscript 2-1 * 2 = a subscript 1 * 2 = -4a * 2 = -8a.

Similarly, for a subscript 3:

a subscript 3 = a subscript 3-1 * 2 = a subscript 2 * 2 = -8a * 2 = -16a.

By applying the recursive formula repeatedly, we can generate the terms of the sequence. Each term is obtained by multiplying the previous term by 2.

Learn more about recursive formula here:

https://brainly.com/question/1470853

#SPJ11

The probability of getting at least one head is 15/16.

What is probability?

The ratio of positive outcomes to all possible outcomes of an event is known as the probability.

Formula for probability = favourable outcomes/ total outcomes

Main body:

if 4 coins are tossed , total no. of outcomes = 2⁴ = 16

In a toss there are 2 outcomes T or H

so, Probability of getting Head = 1/2

The probability of getting at least 1 head = 1- probability of getting no heads

⇒1 - Probability of getting tail in 4 tosses

⇒ 1 - (1/2)⁴

⇒ 1 - 1/16

⇒ 15/16

So the probability of getting at least one head is 15/16.

to learn more about probability click on the link below.

https://brainly.com/question/24756209

#SPJ4

In a perfectly competitive industry, the demand curve is negatively sloped. so, the correct option is d) Negatively Sloped

In economics, the concept of demand curve plays a crucial role in understanding how prices and quantities of goods or services interact. In a perfectly competitive industry, where there are many buyers and sellers, each having negligible market power, the demand curve takes on a specific shape based on the behavior of buyers in the market.

The demand curve represents the relationship between the price of a product and the quantity demanded by consumers in a particular market. In a perfectly competitive industry, all firms produce identical goods or services, and buyers have access to perfect information. This means that buyers are fully aware of the prices charged by all sellers in the market.

a) Evenly divided: In a perfectly competitive market, the demand curve is not evenly divided. Each individual buyer's demand is a small fraction of the total market demand. However, when we consider the entire market, the demand curve takes on a specific shape.

b) Horizontal: The demand curve in a perfectly competitive industry is not horizontal. A horizontal demand curve would imply that buyers are willing to purchase an unlimited quantity of a good or service at a particular price. However, in reality, buyers have limitations on their purchasing power and preferences.

c) Directly sloped: The demand curve in a perfectly competitive industry is not directly sloped. A directly sloped demand curve would indicate a constant increase or decrease in quantity demanded as the price changes. However, this is not the case in a perfectly competitive industry.

d) Vertical: The demand curve in a perfectly competitive industry is not vertical. A vertical demand curve would imply that the quantity demanded remains constant, regardless of changes in price. In a perfectly competitive market, buyers are generally sensitive to changes in price, which affects the quantity demanded.

e) Negatively sloped: The most appropriate choice for the shape of the demand curve in a perfectly competitive industry is "negatively sloped." In a perfectly competitive market, the demand curve slopes downward from left to right. This means that as the price of a good or service increases, the quantity demanded by buyers decreases, and vice versa. This negative relationship between price and quantity demanded is a fundamental characteristic of the demand curve in a perfectly competitive market.

To summarize, in a perfectly competitive industry, the demand curve is negatively sloped. As the price increases, the quantity demanded by buyers decreases, and as the price decreases, the quantity demanded increases. This behavior reflects the underlying relationship between price and consumer demand in a competitive market.

To know more about Demand Curve here

https://brainly.com/question/29307412

#SPJ4

Complete Question:

We expect the demand curve in the perfectly competitive industry to be Group of answer choices

a) evenly divided

b) horizontal

c) directly sloped

d) vertical

e) negatively sloped.

Answer:

SAS

Step-by-step explanation:

The measure of angle D is, 67.4°.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

In triangle DEF, DE = 21, EF = 24, and DF = 26.

By the formula, we get;

⇒ sin θ = Opposite / Hypotenuse

Substitute all the values, we get;

⇒ sin D = 24/26

⇒ sin D = 0.9430

⇒ ∠D = sin⁻¹ (0.9430)

⇒ ∠D = 67.4°

Thus, The measure of angle D is, 67.4°.

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ1

Answer:

ss

Step-by-step explanation:

sas

The radius of the circle who center is at ( 5 , 2 ) and the point on the circle is ( -3 , 4 ) is given by r = 2√17 units

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the radius of the circle be r

Let the center of the circle be A ( 5 , 2 )

Let the point on the circle be P ( -3 , 4 )

Now , standard form of a circle is

( x - h )² + ( y - k )² = r²

So , r² = ( 5 - ( -3 ) )² + ( 2 - 4 )²

On simplifying the equation , we get

r² = ( 8 )² + ( 2 )²

r² = 64 + 4

r² = 68

Taking square roots on both sides , we get

r = √68

r = 2√17

Hence , the radius of the circle is 2√17 units

To learn more about circle click :

https://brainly.com/question/28391204

#SPJ2

Answer: 6 bricks long by 6 bricks wide

Step-by-step explanation:

Since her first arrangement is a 12 x 3 brick patio, we can assume she has 36 bricks. A square has equal lengths of all sides, with this info, she can arrange the 36 bricks into a 6 by 6 patio

The probability that at most two customers purchase the investment is 0.1875 or 18.75%.

To calculate the probability that at most two customers purchase the investment,  to calculate the probabilities for each possible outcome: 0, 1, and 2 customers purchasing the investment, and then sum them up.

Let's consider the customers as A, B, C, and D, with D being the fourth customer.

Probability of 0 customers purchasing:

P(0 customers) = (1 - probability of sale)²number of customers

= (1 - 0.5)²4

= 0.0625

Probability of 1 customer purchasing:

P(1 customer) = (probability of sale)²1 ×(1 - probability of sale)²3 (since 3 customers won't purchase)

= 0.5²1 ×0.5²3

= 0.5 × 0.125

= 0.0625

Probability of 2 customers purchasing:

P(2 customers) = (probability of sale)²2 × (1 - probability of sale)²2 (since 2 customers will purchase)

= 0.5²2 ×0.5²2

= 0.25 × 0.25

= 0.0625

Now  sum up these probabilities to find the probability that at most two customers purchase the investment:

P(at most 2 customers) = P(0 customers) + P(1 customer) + P(2 customers)

= 0.0625 + 0.0625 + 0.0625

= 0.1875

To know more about probability  here

https://brainly.com/question/32117953

#SPJ4

Answer:

117°

Step-by-step explanation:

Start by finding the measure of the angle adjacent to the one marked 101 degrees. Since they are a linear pair, they add up to 180 therefore...

101+y=180

Subtract 101 from both sides...

y=79

Now, using the exterior angle theorem (the exterior angle is equivalent to the sum of the two interior angles that are NOT adjacent to the exterior angle), we can set up an equation to find x...

x=38+79

x=117

Answer: -31

Step-by-step explanation:

5x³- 3x + 2 = 0

a = 5, b = -3, c = 2

(-3)² -4 × 5 × 2

-31

A. The total charge in the device at t = 1 s is 28(1 + e⁻²¹) × 10⁻³ mC.

B. The power consumed by the device at t = 1 s is 27 sin(44) × 28(1 + e⁻²¹) mW.

To calculate the total charge in the device at t = 1 s, we need to integrate the current over time.

Given:

v(0) = 27 sin(44) V

i(0) = 28(1 + e⁻²¹) mA

We'll convert the current to amperes for consistency:

i(0) = 28(1 + e⁻²¹) × 10^(-3) A

We integrate the current from t = 0 to t = 1 s to find the total charge:

q(t) = ∫[0 to t] i(t') dt'

Since q(0) = 0, we can write:

q(t = 1) = ∫[0 to 1] i(t') dt'

Let's perform the integration:

q(t = 1) = ∫[0 to 1] 28(1 + e⁻²¹) × 10⁻³ dt'

= 28(1 + e⁻²¹) × 10⁻³ ∫[0 to 1] dt'

= 28(1 + e⁻²¹) × 10⁻³ [t'] [0 to 1]

= 28(1 + e⁻²¹) × 10⁻³ (1 - 0)

= 28(1 + e⁻²¹) × 10⁻³ mC

Therefore, the total charge in the device at t = 1 s is 28(1 + e⁻²¹) × 10⁻³ mC.

B. To calculate the power consumed by the device at t = 1 s, use the formula:

P(t) = v(t) × i(t)

Given v(0) = 27 sin(44) V and i(0) = 28(1 + e⁻²¹) mA, we need to evaluate v(t) and i(t) at t = 1 s:

v(t = 1) = 27 sin(44)

i(t = 1) = 28(1 + e⁻²¹)

Now we can calculate the power:

P(t = 1) = v(t = 1) × i(t = 1)

= 27 sin(44) × 28(1 + e⁻²¹)

Therefore, the power consumed by the device at t = 1 s is 27 sin(44) × 28(1 + e⁻²¹) mW.

learn more about charge and power: https://brainly.com/question/874116

#SPJ4

The complete question goes thus:

The voltage v1) across a device and the current i(t) through it are (0) = 27 sin(44) V and (0) = 28(1 + e-21) mA.

Calculate the total charge in the device at t = 1 s, assuming q(0) = 0. The total charge in the device at t = 1 s is ___ mC.

Calculate the power consumed by the device at t = 1 s. The power consumed by the device at t = 1 s is ___ mW.

The appropriate units for the rate of change in this case are dollars per unit, since we are measuring the change in price per unit of change in the number of units sold. Therefore, the answer is "Dollars per unit".

To find the average rate of change of Demand between 40 and 175 units sold, we need to calculate the difference in price per unit at these quantities and divide by the difference in units sold.

Step 1: Calculate D(40) and D(175) using the Demand function.
\(D(40) = -0.0003(40)^2 - 0.04(40) + 23.56\)
\(D(175) = -0.0003(175)^2 - 0.04(175) + 23.56\)

Step 2: Compute the differences in price per unit and units sold.
ΔD = D(175) - D(40)
Δq = 175 - 40

Step 3: Calculate the average rate of change.
Average rate of change = ΔD / Δq

The appropriate units for the rate of change are dollars per unit, per unit, as the change in price per unit is being divided by the change in the number of units sold.

To know more about average rate of change refer here:

https://brainly.com/question/28744270

#SPJ11

The original dimensions of the field are -

L = (7/2)x

B = (7/2)y

Given is that the scale for the drawing of a rectangular playing field is :

2 inches = 7 feet.

We can write the original dimensions of the field as -

L = (7/2)x

B = (7/2)y

Therefore, the original dimensions of the field are -

L = (7/2)x

B = (7/2)y

To solve more questions on scale factor, visit the link -

brainly.com/question/30098550

#SPJ1

Answer:

x = 68

Step-by-step explanation:

The formula for calculating the sum of interior angles of a polygon is: (n - 2) x 180° (where n is the number of sides)

This polygon has 5 sides, so the sum of the interior angles:

(5 - 2) x 180° = 540°

To find x, add together all the angle expressions, equate to 540 and solve for x:

                                                       U + V + W + Y + Z = 540

                       (x - 8) + (3x - 11) + (x + 8) + x + (2x + 7) = 540

Gather like terms:  x + 3x + x + x + 2x - 8 - 11 + 8 + 7 = 540

Combine like terms:                                           8x -4 = 540

Add 4 to both sides:                                               8x = 544

Divide both sides by 8:                                             x = 68

The measure of angle BAC is of 14.48º, considering the relations in a right triangle.

There are three relations in a right triangle, presented as follows:

Using a ruler, it is found that the length of the opposite side to angle BAC, of CB, is of 1.5 cm, hence the following relation is established, considering the hypotenuse of 6 cm.

sin(x) = 1.5/6

In which x is the measure of angle BAC.

x can be isolated applying the arc sine function, which is the inverse of the sine, hence:

x = arcsin(1.5/6)

x = 14.48º.

More can be learned about the relations in a right triangle at https://brainly.com/question/26396675

#SPJ1

Out of 120 students, 30 students do not participate in sports or music, and 30 students participate in both activities.

Let's solve this using the principle of inclusion-exclusion.

Let A be the event of students playing sports, B be the event of students playing music, and N be the event of students not participating in either activity. We are given that there are 120 students, and 30 students do neither activity (N). Therefore, the number of students who participate in at least one activity is 120 - 30 = 90.

Now, we know that 50 students do not play sports (not A) and 70 students do not play music (not B).

Using the principle of inclusion-exclusion, we can calculate the number of students who participate in both activities as follows:

Students who participate in at least one activity (A ∪ B) = Students who play sports (A) + Students who play music (B) - Students who play both (A ∩ B)

90 = 50 + 70 - Students who play both

By rearranging the equation, we can find that Students who play both (A ∩ B) = 50 + 70 - 90 = 30.

Therefore, there are 30 students who play both sports and music, and 30 students who do not participate in either activity.

To learn more about principle click here

brainly.com/question/4525188

#SPJ11

Answer:

x=67

Step-by-step explanation:

Sum of all angles is 180

36+77+x=180

113+x=180

x=180-113

x=67

PLZZZ MARK ME AS BRAINLIEST

Answer:

Step-by-step explanation:

35368

Answer:

400

Step-by-step explanation:

Let the number be known as "x".

Given statement:

45% of a number is 180.

The term "of" defines multiplication between two terms. In this case, the terms are 45% and the number "x". Therefore,

     ⇒ 45% × x = 180

When we convert a percentage into a fraction, simply divide the percentage by 100 and remove the percentage sign to obtain the result in fraction form.

     ⇒ 45/100 × x = 180

Multiplying 45/100 and x:

     ⇒ 45/100 × x = 180

     ⇒ 45x/100 = 180

Using cross multiplication:

     ⇒ 45x/100 = 180

     ⇒ 45x = 180 × 100

Simplifying the right-hand-side:

     ⇒ 45x = 180 × 100

     ⇒ 45x = 18000

Dividing 45 to both sides of the equation:

     ⇒ 45x = 18000

     ⇒ 45x/45 = 18000/45

     ⇒ x = 18000/45 = 400

Therefore, the number is 400.

The value of the given expression 6/(y-z) - 2/(y-z) is 4/(y-z). Option 3 is the correct answer.

In algebra, like terms are those in which the same variable(s) are raised to the same power (s). Because they both have the same variable (y) raised to the same power, the expressions 2xy and -5y are similar (1). When combining terms that have similar coefficients, it's important to preserve the exponent and variable constants.

The given expression is 6/(y-z) - 2/(y-z).

Simplifying the expression by combining the like terms we have:

(6 - 2)/(y-z) = 4/(y-z)

Hence, the value of the given expression is option 3 4/(y-z).

Learn more about expressions here:

https://brainly.com/question/14083225

#SPJ1

Answer:

8

Step-by-step explanation:

Let x = the unknown no.

Then

\(\frac{50}{20} = \frac{20}{x}\)

50x = 400

 x = 8

If the geometric mean of two numbers is 20, one number is 50 then the other number is 8

"The geometric mean is the average rate of return of a set of values calculated using the products of the terms."

Formula to calculate geometric mean is

\(GM = \sqrt{x_{1}.x_{2} }\)

Here,

GM = 20

\(x_{1}=50\\ x_{2} =?\)

Substitute the values in the formula

\(20=\sqrt{50.x_{2} }\)

Squaring on both sides

\(400=50(x_{2})\\ x_{2} =\frac{400}{50} \\x_{2}=8\)

Hence, the other number is 8.

To learn more about Geometric Mean here

https://brainly.com/question/10668117

#SPJ2

The company's profit from selling 22,000 radios is $ 30,000

a. The company's profit function is P(x) = R(x) - C(x)

Profit is the difference between the revenue and the cost.

The profit function is given by P(x) = R(x) - C(x).

The cost function is C(x) = 80,000 + 34x,

and the revenue function is R(x) = 39x.

Substituting the given values of C(x) and R(x), we have;

P(x) = R(x) - C(x)P(x)

      = 39x - (80,000 + 34x)P(x)

      = 5x - 80,000b

The company's profit from selling 22,000 radios is $ 10,000.

The company's profit function is P(x) = 5x - 80,000.

We are to find the company's profit if 22,000 radios are produced and sold.

To find the profit from selling 22,000 radios, we substitute x = 22,000 in the profit function.

P(22,000) = 5(22,000) - 80,000P(22,000)

                 = 110,000 - 80,000P(22,000)

                 = $30,000

Therefore, the company's profit is $ 30,000.

To know more about profit function refer here:

https://brainly.com/question/33580162

#SPJ11

Answer:

The numbers are 2 and 3. 2^2+3^2=4+9=13

Step-by-step explanation:

Answer:

13 is your answer.

let two no. be x and y

by question

x+y=5

x=5-y...........(1)

xy=6.............(2)

putting the value of x in equation 2) we get

(5-y)y=6

5y-y²=6

y²-5y+6=0

y²-3y-2y+6=0

y(y-3)-2(y-3)=0

(y-3)(y-2)=0

either

y=3

or

y=2

putting the value of y in equation 1

when y=3

x=5-3=2

when

y=2

x=5-2=3

now

when

x=3 y=2

the sum of the square of the numbers=x²+y²=3²+2²=9+4=13

The  correct way to solve this equation for m in terms of y is  m = b - y/x

It is important to note that subject of formula is the variable that is made to stand alone in an equation.

It is described as the variable that is being worked out in an equation.

The subject of formula in an equation is worked to stand alone on on end of the equality sign.

Example of equations

x = y - 2

The variable 'x' is the subject of formula

From the information given, we have that;

y= mx+b

collect the terms

mx = b - y

Divide by the coefficient

m = b - y/x

The equation for m is m = b - y/x

Learn about subject of formula at: https://brainly.com/question/10643782

#SPJ1

The complete question:

The equation y=mx+b is used to express the equation of a line. Which solution is a correct way to solve this equation for m in terms of y?

Answer:

Your answer is A.

Hope this helps!

Step-by-step explanation:

Because g(x) is (-2, 0 ) and (0, 4 ). So the slope is 4/2 or 2. Then you can figure out the equation for g(x) which is g(x) = 2x + 4.

f(x) is (0, 4 ) and (2, 0 ) so the slope is 0 - 4 / 2 - 0 which is -4/2 or -2. Then figure out the equation for f(x) which is f(x) = -2x + 2.

Now with the two equations, you can just go through the answers so

f(0) = 2   ->   f(0) = -2(0) + 2 which equals 2.

g(-2) = 0   ->     g(-2) = 2(-2) + 4  which equals 0.   So this answer is right.

Answer:

B

Step-by-step explanation:

Answer:

4 IS THE ANSWER MATE

Step-by-step explanation:

Absolutely, I can do that!

Let's take a look at each statement:

1) f(x) has a y-intercept at (0,2)

To find the y-intercept, we need to set x to 0 and solve for y. Plugging in x = 0 into the equation for f(x), we get:

f(0) = -log(0+4) + 2

f(0) = -log(4) + 2

f(0) = -0.602 + 2

f(0) = 1.398

Since the y-coordinate of the y-intercept is 1.398, not 2, this statement is false.

2) The function -f(x) has a y-intercept at (0,2)

Since the negative sign in front of f(x) reflects the graph of f(x) across the x-axis, we can determine the y-intercept of -f(x) by taking the opposite of the y-intercept of f(x). Since the y-intercept of f(x) is not 2, this statement is also false.

3) As x approaches positive infinity, the function f(x) approaches negative infinity.

The function f(x) is a logarithmic function with a negative coefficient, which means it approaches negative infinity as x approaches positive infinity. Therefore, this statement is true.

4) As x approaches -4 from the right, the function f(x) approaches negative infinity.

As x approaches -4 from the right, the value of f(x) becomes more and more negative without bound, which means that f(x) approaches negative infinity as x approaches -4 from the right. Therefore, this statement is also true.

In summary, statements (1) and (2) are false, while statements (3) and (4) are true.

Answer:

(f - g)(x) = 3x^5 - 2x^4 - x^2 + x - 11 in standard form.

Step-bystep-Explanation:

To find (f - g)(x), we need to subtract the function g(x) from the function f(x) by subtracting the corresponding terms.

Given:

f(x) = 3x^5 + 6x^2 - 5

g(x) = 2x^4 + 7x^2 - x + 16

To find (f - g)(x), we subtract each term of g(x) from the corresponding term of f(x):

(f - g)(x) = (3x^5 - 2x^4) + (6x^2 - 7x^2) + (-5 - (-x)) - 16

Simplifying this expression, we get:

(f - g)(x) = 3x^5 - 2x^4 + 6x^2 - 7x^2 + (5 + x) - 16

Combining like terms, we have:

(f - g)(x) = 3x^5 - 2x^4 - x^2 + x - 11

Therefore, (f - g)(x) = 3x^5 - 2x^4 - x^2 + x - 11 in standard form.

#SPJ11