What is the distance from the center of the circle C to chord AB?

Step-by-step explanation:

​Erik earns a 4% commission on each car he sells. A car listed at $39,499 sold for $36,800.

A. How much was Erik’s commission? Round your answer to the nearest cent.

4% = 0.04

36,800 * 0.04 = $1,472

Erik's Commission = $1,472

________________________________________

B. How much commission did Erik lose by not selling the car at the original listed price? Round your answers to the nearest cent.

would have made: 39,499 * 0.04 = $1,579.96

$1,579.96 - $1,472 = $107.96

Commission Lost = $107.96

In an experiment on a damped spring oscillator with spring constant n/m, student c obtains the displacement vs time curves as in fig. 2(a), and records the maximum displacement data points as below is y = - 3.7148.

Here we have to find the displacement for the graphs of y and t that is maximum and We can find that by y = mc where m, = slope, c= intercept.

Read more about the slope:

https://brainly.com/question/23946616

#SPJ4

As per the given simple interest, the amount invested in each account is 50000, 60000, and 10000 respectively.

Simple interest:

In math, the method of calculating the interest amount for a particular principal amount of money at some rate of interest is known as simple interest.

Given,

Pierre inherited $506,000 from his uncle and decided to invest the money. He put part of the money in a money market account that earns 4.5% simple Interest. The remaining money was invested in a stock that returned 5% in the first year and a mutual fund that lost 4% in the first year. He invested $10,000 more in the stock than in the mutual fund, and his net gain for 1 yr was $3060.

Here we need to determine the amount invested in each account.

Let us consider the total amount invested on is written as,

=> X+Y+Z = 120000

And according tot he given details we know that,

=> Y = Z + 10000

AS we apply the interest, then we get,

=> 0.022X + 0.06y - 0.02Z = 2820  

Apply the value of y as z + 10000, then  we get,

=> X+(Z+10000) + Z = 120000

=> 0.022X + 0.06(Z+10000) - 0.02Z = 2820

Then we simplify this one then we get,

=> X + 2Z = 110000

=> 0.022X + 0.06Z + 600 - 0.02Z = 2820

=> 0.022(110000 - 2Z) + 0.06Z + 600 - 0.02Z = 2820

=> 2420 - 0.044Z + 0.06Z + 600 - 0.02Z  = 2820

=>3020 - -0.004z = 2820

=> 0.004z = 200

Therefore, the amount invested on the funds are 50000, 60000, and 10000

To know more about Simple interest here.

https://brainly.com/question/22621039

#SPJ1

It is deduced that b and s are not mutually exclusive events as A. No, because the probability of, b intersection s, equals the fraction 5 over 78

Two events are said to be mutually exclusive, if the two events cannot occur simultaneously, hence the intersection of such event defined as (BnS) will be 0.

We can obtain the probability of (BnS) as follows :

n(BnS) = number of students who are both in the band and in the sport team.

Let, this portion of students be represented as x :

(35-x) + (32-x) + x + 16 = 78

35 - x + 32 - x + x + 16 = 78

83 - x = 78

Collect like terms

83 - 78 = x

5 = x

Hence, n(BnS) = 5

Therefore, the probability of B and S will be :

n(BnS) / total number of students

P(BnS) = 5/78

Since, P(BnS) ≠ 0 ; then the events are not mutually exclusive

Learn more about probability on:

https://brainly.com/question/24756209

#SPJ1

The interval of convergence of the given power series is I=[0, 2/9] and the radius of convergence of power series is R=1

The disk of convergence is the set of all places whose distance to an is strictly less than the radius of convergence.

Given, the power series is,

[tex]\sum_{k=1}^{\infty }[/tex] 1/(k²+k)[tex](9x-1)^{k}[/tex]

Let [tex]u_{k}[/tex]=1/(k²+k)

The radius of the convergence is,

R=[tex]\lim_{k \to \infty}[/tex]| [tex]u_{k}[/tex]/[tex]u_{k+1}[/tex]|

=[tex]\lim_{k \to \infty}[/tex] ((k+1)²+(k+1))/(k²+k)

=[tex]\lim_{k \to \infty}[/tex] (k²+3k+2)/(k²+k)

=[tex]\lim_{k \to \infty}[/tex] ((1+(3/k)+(2/k²))/(1+(1/k))=1

The interval of convergence is:

|9x-1|<1

Or, -1<9x-1<1

Or, 0<9x<2

Or, 0<x<2/9

Given the power series is converges in the interval (0, 2/9)

If x=0, then the power series becomes as shown,

[tex]\sum_{k=1}^{\infty }[/tex](1/(k²+k)([tex]-1^{k}[/tex])

Let [tex]a_{k}[/tex]=([tex]-1^{k}[/tex])(1/(k²+k)

[tex]\lim_{k \to \infty}[/tex]  [tex]a_{k}[/tex]=0 and { [tex]a_{k}[/tex]} sequence is monotone decreasing

Hence by Leibnitz's test,

[tex]\sum_{k=1}^{\infty }[/tex](1/(k²+k)([tex]-1^{k}[/tex]) is convergent

If x=2/9 then the power series becomes [tex]\sum_{k=1}^{\infty }[/tex](1/(k²+k)

Let  [tex]a_{k}[/tex]=(1/(k²+k)and let [tex]b_{k}[/tex]=1/k²

Then [tex]\sum_{k=1}^{\infty }[/tex]  [tex]a_{k}[/tex]/ [tex]b_{k}[/tex]

[tex]\sum_{k=1}^{\infty }[/tex] k²/(k²+k)=1 (≠0)

By comparison test, we know that ∑ [tex]a_{k}[/tex] and ∑ [tex]b_{k}[/tex] converge or diverge together.

As  ∑ [tex]b_{k}[/tex]= ∑1/k² converges this implies that  ∑ [tex]a_{k}[/tex]=(1/(k²+k) converges

Hence the interval of convergence of the given power series is,

I=[0, 2/9]

Therefore, the interval is I=[0, 2/9] and the radius of convergence in the power series is R=1.

To know more about radius of convergence, visit:

https://brainly.com/question/18763238

#SPJ4

Answer:

6a= 400

6d=480

Step-by-step explanation:

The required area is 12 cm².

A rectangle is a type of parallelogram having equal diagonals.

All the interior angles of a rectangle are equal to the right angle.

The diagonals of a rectangle do not bisect each other.

The given shape is there on a centimeter square grid.

The side of each square is 1 cm.

Then, it is clear from the figure that it consists of a rectangle of dimensions 4 × 2 and one triangle having height h = 2 cm and base b = 4cm.

Now, the area of the given shape is the sum of the area of the rectangle and the triangle.

It can be written as,

Area of the shape  = Area of rectangle + Area of triangle

                               = length × breadth + 1/2 × base × height

                               = 4 × 2 + 1/2 × 4 × 2

                               = 12

Hence, the area of the given shape is 12 cm².

To know more about rectangle click on,

https://brainly.com/question/25501702

#SPJ1

The required area of the given figure is 12 squared units.

Given that,
A figure has been shown we have to determine the area of the figure,

Surface area is defined as the measure of a region or surface is called as surface area.

Here,
The area of the given figure is given as,
Area = area of the rectangle + area of the larger triangle - area of the small triangle.
Area = 2 × 4 + 1/2 [6 × 2] - 1/2 [2×2]
Area = 8 + 3×2  - 2
Area = 8 + 6 - 2
Area = 14 - 2
Area = 12 squared units.

Thus, the required area of the given figure is 12 squared units.

Learn more about the surface area here: https://brainly.com/question/2835293

#SPJ1

Angle opposite to the equal side of the triangle is always equal here we apply on the vice versa.Thus the length of BC is 17 units.

Given:

Angle B and Angle C are congruent.

The length of the side AC is labeled as x plus 9.

The length of the sides AB is labeled as 2x minus 8.

The length of the side BC is labeled as x.

We know that,

The angle opposite to the equal side of the triangle is always equal.

Therefore,

<B = <C

so

AB = AC

2x - 8 = x + 9

2x - x = 9 + 8

x = 17.

Therefore the length of BC is 17 units.

Learn more about the length here:

https://brainly.com/question/28537063

#SPJ4

Full question:

What is the length of BC? Enter your answer in the box. units triangle ABC with horizontal side BC. Vertex A lies above side BC.Angle B and Angle c are marked congruent.The length of side AC is labeled as x plus 9.The length of side AB is labeled as 2x minus 8.The length of side BC is labeled as x.

Answer:

Yes! The sides 5,3 and 7 can create a triangle!

Step-by-step explanation:

It follows the rule:

a + b > c

a + c > b

c + b > a

The number of coins that has to be collected to have a total score of 1,110 is 6.

The relationship between two variables are directly proportional, if the two variable move in the same direction. If one of the variables increases, the other variable increases. If one of the variables decreases, the other variable decreases.

The equation that is used to represent direct proportion is:

y = kx

Where:

370 = 2k

k = 370 / 2

k = 185

110 = 185x

x = 1110 / 185

x= 6

To learn more about direct variation, please check: https://brainly.com/question/27573249

#SPJ1

The same financial document number range can be assigned to several document types. Financial document number ranges defined at client level should NOT overlap. Financial document number ranges are defined at company code level.

Financial statements are official records of a person, business, or other entity's financial situation and actions. An easy-to-understand style is used to provide pertinent financial data in a systematic manner. Financial papers, usually referred to as financial statements, are used to present financial data about an organization in a consistent way. They come with a cash flow statement, an income statement, and a balance sheet. A balance sheet is a moment in time snapshot of your company's financial health.

To know more about financial document,

https://brainly.com/question/28546447

#SPJ4

Answer:

16.4m

Step-by-step explanation:

Area of a triangle = 1/2bh

A=1/2(6.7)(4.9)

A= 16.4m

After solving, the reaminder is 1 if x^3-2x^2+X+1 is divided by x-1.

In the given question we have to find the remainder if x^3-2x^2+X+1 is divided by x-1.

The given equation is x^3-2x^2+X+1.

We have to divide this equation by x-1 to find the remainder.

To find the remainder we firstly find the value of x from x-1. Then we put the value of x in the given equation then we can easily find the remainder.

Putting the x-1 equla to zero, so

x=1

Now putting the value of x in the given equation.

=x^3-2x^2+X+1

=(1)^3-2(1)^2+1+1

=1-2+1+1

=1

Hence, the remainder is 1 if x^3-2x^2+X+1 is divided by x-1.

To learn more about division method link is here

brainly.com/question/12520197

#SPJ4

Answer:

x = 7

Step-by-step explanation:

3(2x - 10) + 4(x-7)= 12

6x - 30 + 4x - 28 = 12

combine x terms on left side:

10x - 30 - 28 = 12

combine numbers on left side:

10x - 58 = 12

add 58 to both sides:

10x - 58 + 58 = 12 + 58

10x = 70

divide both sides by 10:

10x/10 = 70/10

x = 7

If 15 postage stamps cost $8.25 then 12 stamps will cost $6.6 if all the stamps cost the same amount.

To calculate the cost of 12 stamps we first calculate the cost of one postage stamp by division.

Since 15 stamps cost $8.25 we can calculate the cost of one stamp by dividing the cost of 15 stamps by 15

cost of one stamp = $8.25 ÷ 15

cost of one stamp = $0.55

Since the cost of one stamp is calculated to be $0.55, we can calculate the cost of 12 stamps by multiplication as follows;

cost of 12 stamps = cost of one stamp × 12

cost of 12 stamps = 0.55 × 12

cost of 12 stamps = $6.6

Although a part of your question is incorrect, you might be referring to this question:

Kwai bought 15 postage stamps for $8.25. All stamps cost the same amount. How much will 12 stamps cost?

To learn more about multiplication; click here:

https://brainly.com/question/1135170

#SPJ4

The two numbers are 2 and 4.

What is the greatest common factor?

The highest number that is a factor of all the numbers is known as the greatest common factor of two or more numbers.

Here, we have

Given

Least common multiple of 60 is code for "it's a really small number."

Less than or equal to 12 confirms that the number must be less than 12.

GCF of the two numbers is 2 tells me "it's the smallest number around."

Hence, the two numbers are 2 and 4.  Their multiples can arrive at 60, they are less than 12, and the GCF for both numbers is 2.

To learn more about the greatest common factor from the given link

https://brainly.com/question/219464

#SPJ4

An integer's factors are other integers that, when multiplied, give the same result as the original integer. For instance, 33 and 55 are factors of 1515 since 35=1535=15. Knowing what a factor is, we frequently seek to identify an integer's "factorizations".

An integer is represented as the product of its factors in a factorization. The number 11 and the initial integer are always factors, as you can see. This is referred to as a "prime" or complete factorization of 88. The base number, in this case 22, is therefore prime. A prime integer is one with only itself and the number 11 as components. 11 is not a prime number by definition. Prime factors can be used to factor polynomials. Because the elements x+1x+1 and x+2x+2 are irreducible—they only have 11 and themselves as factors—the second factorization is known as the prime factorization. Similar to factoring integers into a product of integers, each smaller than the original, factoring polynomials aims to describe the original polynomial as a product of polynomials of lower degree.

Learn more about factors here

https://brainly.com/question/26923098

#SPJ4

The 90% confidence interval is [36.19, 39.21]. The population mean of users that are connected at the same time is greater than 35.

What are null hypotheses and alternative hypotheses?

In null hypotheses, there is no relationship between the two phenomenons under the assumption or it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.

The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.

In order to ensure efficient usage of a server, it is necessary to estimate the mean number of concurrent users.

According to records, the average number of concurrent users at 100 randomly selected times is 37.7, with a standard deviation of 9.2.

With this approximation, you can construct the 90% confidence interval the approximate z will be

u± z0.90* σ/[tex]\sqrt{n}[/tex]

z 0.90= 1.64

Then we have

37.7± 1.64*9.2/[tex]\sqrt{100}[/tex]

[36.19, 39.21]

learn more about of standard deviation here

https://brainly.com/question/14006132

#SPJ4

The approximate ratio is 52 to 18 micrograms/ml.

Step 1:

This is a general question in which we need to analyze only the graph.

Regression of the calibration curve of GNE-A in mouse plasma is given.

Step 2:

In the given data, the ratio of area of GNE-A to GNE-B is taken in y axis and GNE - A concentration is taken in x axis. From the graph, it is clear that the concentration of GNE-A corresponding to the GNE-A to GNE-B ratio 52 is 18.

The approximate ratio of areas for gne-a to gne-b when the gne-a concentration is 18 micrograms/ml is 52 : 18.

Learn more about Ratio here:

https://brainly.com/question/2914376

#SPJ4

The required expression gives the rate of change will be d'(3) at which the depth is changing at 3 minutes.

Let d(t) represent the depth of the rain puddle at any time t,

⇒ d(t)  ....(i)

The depth is changing with respect to time, which is given in the question

Differentiate equation (i) with respect to t and we get

⇒ δd(t)/δt = d'(t) ....(ii)

This is the rate of change in depth unit time

As per the question, the depth is changing at 3 minutes

Substitute the value of t = 3 in equation (ii), and we get

⇒ d'(3)

Therefore, the required expression gives the rate of change will be d'(3).

To learn more about the differentiation click here:

https://brainly.com/question/24898810

#SPJ1

(a)The precise expression is

P (X > 1) = 1 − P(X ≤ 1) = 1 − Σ (365/x) x (1/512)^x x (511/512)^365-x

(b) The normal or the Poisson approximate for p(x>1) is

P(X > 1) = 1 − P(X ≤ 1) = 1 – Σe^-365/512. (365/512)^x/x!=0.1603

Probability is the branch of mathematics regarding numerical descriptions of how probable an occasion is to occur, or how possible it is that a proposition is genuine. The probability of an event is a number between zero and 1, wherein, kind of talking, zero suggests the impossibility of the occasion and 1 indicates fact.  

The better the possibility of an occasion, the more likely it is that the event will occur. An easy example is the tossing of an honest (impartial) coin. since the coin is fair, the two results ("heads" and "tails") are both similarly likely; the possibility of "heads" equals the probability of "tails"; and given that no different effects are viable, the chance of either "heads" or "tails" is half off (which could also be written as 0.5 or 50%).

To learn more about probability visit here:

brainly.com/question/14210034

#SPJ4

A provision that ensures performance fees are not earned until the value of a fund exceeds its previous highest level is referred to as High-water mark

A high-water mark is the highest peak in value that an investment fund or account has reached. This term is often used in the context of fund manager compensation, which is performance-based.

The high-water mark ensures the manager does not get paid large sums for poor performance. If the manager loses money over a period, he must get the fund above the high-water mark before receiving a performance bonus

With a high-water mark, the investor pays a fee that only covers the amount the fund earned between the point of entry and its highest level.

The high-water mark prevents this "double fee" from occurring.

To know more about High-water mark here

https://brainly.com/question/17779110

#SPJ4

Answer:

x=21.1

Step-by-step explanation:

m1 + m2 = 180

(4x-11)+(6x-20)=180

10x-31=180

x=21.1

Two symbols are used in the expressions of three-part inequalities. Three-part inequality solutions are equivalent to two-part inequality equation solutions.

Solve the −4≤2x−1≤5-4≤2x-1≤5 equation.

Try to obtain x on your own then.

To the three sides, add one.

−4+1≤2x−1+1≤5+1-4+1≤2x-1+1≤5+1

−3≤2x≤6-3≤2x≤6

By dividing all three sides by 2, you get 1.5x3 (32 2 x 2 x 62).

Learn more about equation here

https://brainly.com/question/29538993

#SPJ4

The combined area is 0.9545.

Given:

The area under the normal curve to the left of z=-2 plus the area

under the normal curve to the right of z = 2.

Area under the normal curve to the left of z = -2 is:

= 0.0228

Area under the normal curve to the right of z = 2

= 0.9772

Combined area is = 0.9545

Therefore The combined area is 0.9545.

Learn more about the area here:

https://brainly.com/question/27683633

#SPJ1

Answer:y=1/3x+15

Step-by-step explanation: the slope is already given you just take the y-intercept from your ordered pair and plug it in

The y -intercept of the exponential function is; 2

The y -value of the solution in Quadrant I is; 5

The number of points of intersection is; 1

The y -intercept of the linear function is; 7

We are given the functions as;

Exponential function: y = 4ˣ + 1

Linear Function: y = -2x + 7

1) The y-intercept of the exponential function will be the point at which x = 0. Thus;

y = 4⁰ + 1

y = 1 + 1

y = 2

2) From the attached graph, we see that the coordinates of intersection in Quadrant 1 is; (1, 5)

Thus, the y-value is 5

3) The number of points of intersection of the linear and exponential function is; 1 point

4) The y-intercept of the linear function is the value of y when x = 0. Thus;

y = -2(0) + 7

y = 7

Read more about Linear and Exponential functions at; https://brainly.com/question/1594165

#SPJ1

The average field strength in current carrying wire placed between the poles of a strong magnetic field is 1.46 T.

The formula to be used for calculation is -

B = F/(I×L×Sin theta), where B is magnetic field density, F is force, I is current and l is length.

Keep the values in formula -

Converting length to m. 1 m is 100 cm.

3.5 cm = 0.035 m

B = 2.17 / (42.5 × 0.035 × sin 90)

Performing multiplication on Right Hand Side of the equation

B = 2.17 / 1.49

Performing division on Right Hand Side of the equation

B = 1.46 T

Hence, the magnetic field is 1.46 T.

Learn more about magnetic field -

https://brainly.com/question/14411049

#SPJ4

The complete question is -

A wire carrying a 30.0-A current passes between the poles of a strong magnet that is perpendicular to its field and experiences a 2.16-N force on the 4.00 cm of wire in the field. What is the average field strength

Answer: 14) 1.5, 15) 5/8, 16) 1/6

Step-by-step explanation:

For the first one, you want to find the least common denominator. The least common denominator is 10, so you multiply the numerator and denominator to get 9/10+6/10=15/10. 15/10 is 1.5 or 1 1/2

for the 2nd one you do the same thing. You can get 1/4 to have a denominator of 8 by converting it to 2/8. 7/8-2/8=5/8

finally, you can change 2/3 to 4/6 to get a common denominator. 5/6-4/6=1/6.

Answer:  For Number (14)    1  1/2

Step-by-step explanation:

Exact Form:

3/2

Decimal Form:

1.5

Mixed Number Form:

1  1/2

The pool area measures the following dimensions:

Length = 58 feet.

Width = 30.5 feet.

Equations are used to express the data since the 119-foot fence should only contain three sections of the pool (two wide and one long).

First, a calculation that determines the total number of feet in the fence

X + 2Y = 119 (where X is the length and Y is the width)

X = 2Y-3 (because the length is 3 feet less than twice the width)

We proceed to solve for Y using these equations to replace the second equation in the first equation:

X + 2Y = 119

2Y -3 + 2Y = 119

4Y - 3= 119

4Y= 122

Y = 122/4, and Y = 30.5 feet.

We apply the second equation to determine the value of X because we already know that the width equates to 30.5 feet: X = 2Y-3 X = 2 (30.5)-3 X = 61 - 3 X = 58

It can be seen from this that the length is 58 feet.

As a result, the pool area measures Length = 58 feet and Width = 30.5 feet.

To learn more about width click here:

brainly.com/question/17156323

#SPJ4