the monthly utility bills in a city are normally distributed with a mean of $70 and a standard deviation of $8. find the monthly utility bill (i.e. the x-value) that corresponds to a z-score of -0.75. do not round and do not include the $ sign.

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: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

(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

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 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

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

An example of an obtuse angle is 135°.

When two straight lines or rays intersect at a shared terminal, an angle is generated.

An angle whose measure is more than 90° but less than 180° is said to be an obtuse angle.

Therefore, an example of an obtuse angle is 135°.

Learn more about the angle:

https://brainly.com/question/28451077

#SPJ1

Answer:

6a= 400

6d=480

Step-by-step explanation:

Yes, leading coefficient and degree of the polynomial functions can affect the behavior of its graph. Because of the positive leading coefficient, the graph ascends to the right. To ascertain the behavior, consider the function's degree and the sign of the leading coefficient.

The term with the greatest x power is the leading term in a polynomial function. The leading coefficient is the coefficient of the leading phrase.

Given,

Yes, leading coefficient and degree of the polynomial functions can affect the behavior of its graph.

The graph's final behavior is determined by a polynomial function's degree and leading coefficient. For very big or very small values, the leading coefficient is more important than the other function coefficients. The coefficient of the leading term is the leading coefficient in a polynomial. Because of the positive leading coefficient, the graph ascends to the right. To ascertain the behavior, consider the function's degree and the sign of the leading coefficient.

To learn more about leading coefficient, visit:

https://brainly.com/question/15323309

#SPJ4

Answer: 110°

Step-by-step explanation: We know that a quadrilateral is always 360° in total, and two of the angles are right angles, which both equal 90°. We also know that one of the angles is 70° so, with this information, we can set up an equation. 90+90+70+x=360 To solve this, add 90, 90, and 70 together. This equals 250. Now we subtract 360 and 250, which equals 110°.

hope this helps!

please give brainliest!                                  

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

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 equation of a line given two points in point slope form is:

y - y1 = (y2-y1 / x2-x1)(x-x1).

Given:

Two points (x1,y1) and (x2,y2)

we know that,

slope m = y2-y1 / x2-x1

the equation passes through (x1,y1).

we know that:

Point slope form is y - y1 = m(x-x1)

substitute m value

y - y1 = (y2-y1 / x2-x1) (x-x1)

Therefore The equation of a line given two points in point slope form is:

y - y1 = (y2-y1 / x2-x1)(x-x1).

Learn more about the equation here:

https://brainly.com/question/10413253

#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

Answer:

16.4m

Step-by-step explanation:

Area of a triangle = 1/2bh

A=1/2(6.7)(4.9)

A= 16.4m

The answer is 3/25

The calculation as follows.

First, convert to fraction version of the decimals.

0,12 means 12/100

Second, simplify both up and bottom value of the fraction by dividing it with 4

(12:4)/(100:4) = 3/25

So, the answer is 3/25

Read more on fraction here

https://brainly.com/question/10354322?referrer=searchResults

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

The pair of triangles in the option B are congruent by AAS congruence theorem.

What is AAS congruence theorem ?

The Triangles Are Congruent Theorem (AAS) states that if two angles and a non-included side in one triangle are congruent to two angles and the matching non-included side in another triangle.

AAS congruence theorem full form is Angle Angle Side .

This means 2 angles 1 side have to be same for the two triangles to be congruent.

So, in the option B, the 2 angles and 1 side same for the two triangles .

To learn more about the AAS congruence theorem  from the given link

https://brainly.com/question/3168048

#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

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

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

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

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

The probability the class average is less than 79 is 0.1587.

What is Normal Distribution ?

Given that,

Normally distributed with a mean μ = 80

sample standard deviation σ = 6

In a class, number of students n = 30   (This may be 36 in ques but we take 30 as mentioned in question )

Let, x = be the individual score

∑x = be the class average

It's given, class average is less than 79.

Now, the probability that the class average is less than 79.

P(∑x < 79) = P( (∑x - μ) / (σ/√n)  < (79 - 80) / (6 /√30) )

                = P( (∑x - μ) / (σ/√n)  < (-1) / 1.09 )

                = P( (∑x - μ) / (σ/√n)  < -1 )     [Round off the Denominator it gives 1]

we know, Standard normal distribution Z = (∑x - μ) / (σ/√n)

so,

P(∑x < 79) = P( Z < -1 )

By Standard normal distribution table,

P( Z < -1 ) = 0.1587

Hence, the probability the class average is less than 79 is 0.1587.

To read more about Normal Distribution

https://brainly.com/question/23418254

#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: 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 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

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 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

Answer:

x=21.1

Step-by-step explanation:

m1 + m2 = 180

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

10x-31=180

x=21.1