Which confidence level will yield the interval that we are most confident in containing the actual value of the population parameter?
a. 99.2%
b. 99.5%
c. Our confidence in whether an interval actually contains the parameter is not affected by the choice of confidence level.
d. 99.9%

From the odd-degree terms, take out one copy and rewrite the series as

[tex]1+6x+x^2+6x^3+\cdots=(1+x+x^2+x^3+\cdots)+5x+5x^3+\cdots[/tex]

[tex]1+6x+x^2+6x^3+\cdots=(1+x+x^2+x^3+\cdots)+5x(1+x^2+\cdots)[/tex]

Then if |x| < 1, we can condense this to

[tex]\displaystyle\sum_{n=0}^\infty x^n+5x\sum_{n=0}^\infty x^{2n}=\frac1{1-x}+\frac{5x}{1-x^2}=\frac{1+6x}{1-x^2}[/tex]

Since the series we invoked here converge on -1 < x < 1, so does this one.

The explicit formula of the function f(x) is [tex]f(x) = \frac{1 + x + 5x}{1-x^2}[/tex]

The function definition is given as:

[tex]f(x) = 1 + 6x + x^2 + 6x^3 + x^4 + ...[/tex]

Expand the terms of the expression

[tex]f(x) = 1 + 5x + x + x^2 + 5x^3 + x^3 + x^4 + ...[/tex]

Split

[tex]f(x) = (1 + x + x^2 +x^3 + .....) + 5x + 5x^3 + .. ...[/tex]

Factor out 5x

[tex]f(x) = (1 + x + x^2 +x^3 + .....) + 5x(1 + x^2) + .. ...[/tex]

Express 1 as x^0

[tex]f(x) = (x^0 + x + x^2 +x^3 + .....) + 5x(1 + x^2) + .. ...[/tex]

Express x as x^1

[tex]f(x) = (x^0 + x^1 + x^2 +x^3 + .....) + 5x(1 + x^2) + .. ...[/tex]

Also, we have:

[tex]f(x) = (x^0 + x^1 + x^2 +x^3 + .....) + 5x(x^0 + x^2) + .. ...[/tex]

Rewrite the series using the summation symbol

[tex]f(x) = \sum\limits^{\infty}_{n=0}x^n+ 5x\sum\limits^{\infty}_{n=0}x^{2n}[/tex]

The sum to infinity of a geometric progression is:

[tex]S_{\infty} = \frac{a}{1- r}[/tex]

Where:

a represents the first term, and r represents the common ratio

Using the above formula, we have:

[tex]\sum\limits^{\infty}_{n=0}x^n = \frac{1}{1 - x}[/tex]

[tex]5x\sum\limits^{\infty}_{n=0}x^{2n} = 5x * \frac{1}{1 - x^2} = \frac{5x}{1-x^2}[/tex]

So, we have:

[tex]f(x) = \frac{1}{1-x}+ \frac{5x}{1-x^2}[/tex]

Take the LCM

[tex]f(x) = \frac{1 + x + 5x}{1-x^2}[/tex]

Evaluate the like terms

[tex]f(x) = \frac{1 + 6x}{1-x^2}[/tex]

Hence, the explicit formula of the function f(x) is [tex]f(x) = \frac{1 + x + 5x}{1-x^2}[/tex]

Read more about geometric series at:

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Answer:

False

Step-by-step explanation:

A tessellation refest to a shape that is repeated over and over again covering a plane without any gaps or overlaps. The statement is false given that regular tessellations use only one polygon. Semi-regular tessellations are created with more than one type of regular polygon.

Answer:

x = $0.50

y= $0.75

Step-by-step explanation:

1. Multiply the equations to have the same coefficients

5(6x + 6y = 7.5) → 30x + 30y = 37.5

3(10x + 5y = 8.75) → 30x + 15y = 26.25

2. Subtract the equations

 30x + 30y = 37.5

- 30x + 15y = 26.25

15y = 11.25

3. Solve for y by dividing both sides by 15

y = 0.75

4. Plug in 0.75 for y into one of the equations

6x + 6(0.75) = 7.5

5. Simplify

6x + 4.5 = 7.5

6. Solve for x

6x = 3

x = 0.5

Answer:

The cost of one apple is $0.5

The cost of one orange is $0.75

Step-by-step explanation:

Given information

The cost of an apple = [tex]x[/tex]

The cost of an orange = [tex]y[/tex]

Equation to find the values are:

[tex]6x=6y=7.50\\10x+5y=8.75[/tex]

Now, convert the equations to have same coefficient as:

[tex]5(6x=6y=7.50)\\=30x+30y=37.5\\3(10x+5y=8.75)\\=30x+15y=26.25[/tex]

Now, on solving the above equation by subtracting one from another.

We get,

[tex]15y=11.25\\y=0.75[/tex]

Now , put the value of [tex]y[/tex] in one equation to find the value of [tex]x[/tex].

As,

[tex]6x+4.5=7.5\\x=0.5[/tex]

Hence,

The cost of one apple is $0.5

The cost of one orange is $0.75

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Answer:

y+2 = 4(x-6)

Step-by-step explanation:

The point slope equation of a line is

y-y1 = m(x-x1)  where m is the slope and ( x1,y1) is a point on the line

y - -2 = 4( x-6)

y+2 = 4(x-6)

Answer:

[tex] -3n - 7 [/tex]

Step-by-step explanation:

Considering the linear function represented in the table above, to find what output an input "n" would give, we need to first find an equation that defines the linear function.

Using the slope-intercept formula, y = mx + b, let's find the equation.

Where,

m = the increase in output ÷ increase in input = [tex] \frac{-13 - (-10)}{2 - 1} [/tex]

[tex] m = \frac{-13 + 10}{1} [/tex]

[tex] m = \frac{-3}{1} [/tex]

[tex] m = -3 [/tex]

Using any if the given pairs, i.e., (1, -10), plug in the values as x and y in the equation formula to solve for b, which is the y-intercept

[tex] y = mx + b [/tex]

[tex] -10 = -3(1) + b [/tex]

[tex] -10 = -3 + b [/tex]

Add 3 to both sides:

[tex] -10 + 3 = -3 + b + 3 [/tex]

[tex] -7 = b [/tex]

[tex] b = -7 [/tex]

The equation of the given linear function can be written as:

[tex] y = -3x - 7 [/tex]

Or

[tex] f(x) = -3x - 7 [/tex]

Therefore, if the input is n, the output would be:

[tex] f(n) = -3n - 7 [/tex]

Answer:

m = 26+32

Step-by-step explanation:

To determine the total number of miles biked, add the days together

m = 26+32

Answer:

26+32=m

Step-by-step explanation:

That is the general eqaution of this, because u must add both days worth of biked miles together.

Answer:

candles = $400

matches = $20

Step-by-step explanation:

Let cost of candles = $c

Let cost of matches = $m

c = 20 m (20 times m)

c + m = 420

20m + m = 420

21 m = 420

m = 20

c = 20 (20) = 400

Answer:

6a + 12b + 18c

Step-by-step explanation:

To solve, we distribute the 6 to all of the terms inside the parentheses.

[tex]6*a\\6*2b\\6*3c\\6a+12b+18c[/tex]

Our answer is 6a + 12b + 18c. Hope this helps!

Vocabulary:

Distribute: Give shares of something. In math: Divide / give to each term (in this case)

Answer:

6a+12b+18c

Step-by-step explanation:

To create an equivalent expression, we must distribute the 6. Multiply each term inside of the parentheses by 6.

6(a+2b+3c)

(6*a)+(6*2b)+(6*3c)

6*a=6a

6a+(6*2b)+(6*3c)

6*2b=(6*2)b=12b

6a+12b+(6*3c)

6*3c=(6*3)c=18c

6a+12b+18c

The equivalent expression using the distributive property is 6a+12b+18c

Answer:

Probability of orange hat = 0.0833

Step-by-step explanation:

We have to find the probability of getting an orange hat while we randomly choose from 444 pieces of clothing and 333 colors.

So we have to get hat from the clothing and we have to get orange color from the colors. All shirts , pants , socks and hats are in equal numbers and are 111 each. Also purple, blue and orange are 111 each in number.

The probability of getting hats =

                                                   = 0.25

The probability of getting orange =  = 0.333

Final probability = 0.25 0.333

                          = 0.0833

Answer: 1/12

Step-by-step explanation:

I just had khan academy

Answer:

Step-by-step explanation:

From the information given:

For Adult Men

Mean [tex]\mu[/tex] = 69.5

Standard deviation [tex]\sigma[/tex] = 2.4

observed value X = 74

For Adult Women

Mean [tex]\mu[/tex] = 63.8

Standard deviation [tex]\sigma[/tex] = 2.6

observed value X = 70

Therefore ; the values for their z  scores can be obtained in order to determine who is more unusually tall within his or her respective sex

For Adult Men :

[tex]z = \dfrac{X- \mu}{\sigma}[/tex]

[tex]z = \dfrac{74- 69.5}{2.4}[/tex]

[tex]z = \dfrac{4.5}{2.4}[/tex]

z = 1.875

For Adult Women :

[tex]z = \dfrac{X- \mu}{\sigma}[/tex]

[tex]z = \dfrac{70- 63.8}{2.6}[/tex]

[tex]z = \dfrac{6.2}{2.6}[/tex]

z = 2.3846

Thus; we can conclude that , the women is more unusually tall within his or her respective sex

Answer:

[tex]\Large \boxed{-\dfrac{5}{4}(x+3)(x+1)(x-2)}[/tex]

Step-by-step explanation:

Hello,

Based on the indication, we can write this polynomial as below, k being a real number that we will have to identify (degree = 3 and we have three zeroes -3, -1, and 2).

   [tex]\Large \boxed{k(x+3)(x+1)(x-2)}[/tex]

We know that the point (1,10) is on the graph of this function, so we can say.

[tex]k(1+3)(1+1)(1-2)=10}\\\\4*2*(-1)*k=10\\\\-8k=10\\\\k=\dfrac{10}{-8}=-\dfrac{5}{4}[/tex]

Then the solution is:

[tex]\large \boxed{-\dfrac{5}{4}(x+3)(x+1)(x-2)}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

d. 5250 pounds

Step-by-step explanation:

25 lbs per day

There are 30 days in april

25 lbs/ day * 30 days

1 tiger would eat 750 lbs

There are 7 tigers

7 * 750 =5250 lbs

Answer:

D. 5250 pounds

Step-by-step explanation:

What you need to do is multiply 25 pounds by 30 because there are 30 days in the month of April.

25 x 30 = 750

Then multiply that amount by seven because there are 7 tigers.

750 x 7 = 5250

Answer:

x= 155°

straight line equals 180°

since you have a side that equals to 25°

you subtract

180°-25° = 155°

Answer:

5%

Step-by-step explanation:

Well let’s make a fraction 2/40.

So we have to simplify it to 1/20.

And we do 1 / 20.

So 1 / 20 is .05.

To make this a percent we put the seminal place 2 places to the right.

So the percent is 5%.

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The statement for [tex]6x - 3 = 9[/tex] is :

[tex]\boxed{Six (x) .minus. Three .equals. Nine.}[/tex]

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Hope this helped you.

Could you maybe give brainliest..?

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Answer:

"B. about half the days in march had average temperatures either below 60 or above 73 degrees"

Step-by-step explanation:

To answer this question, note that a box plot is usually divided into quartiles, each representing approximately 25% each.

In the box plot above,

*about 25% (Q1) represents days with temperature of 60° and below. This is about ¼ of the days in March.

*About 25% (Q2) represents days with temperature between 61° and 68°. That's about ¼ of the days in March

*About 25% (Q3) represents days with temperature between 70° and 73°. That's about ¼ of the days in March

*About 25% (Q4) represents days with temperature between 74° and 82°. That's about ¼ of the days in March

*Coldest day in March has a temperature of 54°

*Hottest day in March is 82°

From the options given, the only statement that is true is "B. about half the days in march had average temperatures either below 60 or above 73 degrees"

¼ of the Days in March has temperatures below 60° (Q1), while ¼ of the days in March has temperatures above 73° (Q4). Therefore, ¼+¼ = ½ of the days in March having average temperatures either below 60 or above 73 degrees.

Answer:

b

Step-by-step explanation:

About half of the days in March had average temperatures either below 60 or above 73 degrees.

Answer: i believe it’s 0.28, but tbh i’m on a unit test so i can’t see what’s wrong and what’s right. good luck!

Step-by-step explanation:

Answer:

c- 0.28

Step-by-step explanation:

Answer:

F, J, and K

Step-by-step explanation:

The others are negative so they can't be exponential

The exponential function can't be negative or irrational, so options A, D, and E are correct.

The exponential function in mathematics is represented by the symbol eˣ (where the argument x is written as an exponent). The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to complex numbers or adapted to other mathematical objects like matrices or Lie algebras. The idea of exponentiation, or repeated multiplication, is where the exponential function got its start, but more recent definitions—there are several that are equivalent—allow it to be rigorously extended to all real arguments, including irrational values.

As we discussed above, the exponential function can't be negative or irrational  so, look at the options only,

f(x) = 10(1/7)ˣ,

j(x) = 8(4.13)ˣ,

k(x) = 12(8)ˣ are the exponential functions, whereas

g(x) = 4(-3)ˣ,

h(x) = 4(-13)ˣ are negative, so they can't be exponential functions.

To know more about exponential functions:

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#SPJ2

If the path is perpendicular to the field it is zero.

If the path is along the field it is positive or negative depending on it's direction.

See the attached picture.

Answer:

a

   The Null hypothesis is  [tex]H_o : p = 0.01[/tex]

   The defect did not exceed 0.01

b

   The  95%  confidence interval is   [tex]0.004801 < p < 0.020199[/tex]

   Yes the CI agrees with the result in a  because the value 0.01 fall within the CI

Step-by-step explanation:

From the question we are told that

     The sample size is  n = 800

      The number of defective calculators is  k =  10

       The population is  [tex]p = 0.01[/tex]

The Null hypothesis is  [tex]H_o : p = 0.01[/tex]

The Alternative hypothesis is  [tex]H_a : P> 0.01[/tex]

Generally the proportion of defective calculators is mathematically represented as

         [tex]\r p = \frac{k}{n}[/tex]

substituting values

          [tex]\r p = \frac{10}{800}[/tex]

          [tex]\r p = 0.0125[/tex]

Next is to obtain the critical value of  [tex]\alpha[/tex] from the z-table.The  value is  

          [tex]Z_{\alpha } = 1.645[/tex]

Now the test statistics is mathematically evaluated as

        [tex]t = \frac{\r p - p }{ \sqrt{ \frac{p (1- p )}{n} } }[/tex]

substituting values

          [tex]t = \frac{ 0.0125 - 0.01 }{ \sqrt{ \frac{0.01 (1- 0.01 )}{800} } }[/tex]

           [tex]t = 0.71067[/tex]

Now comparing the values of  t to the value of [tex]Z_{\alpha }[/tex] we see that [tex]t < Z_{\alpha }[/tex] hence we fail to reject the null hypothesis

Generally the margin of error is mathematically represented as  

       [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p (1-\r p )}{n} }[/tex]

where  [tex]Z_{\frac{\alpha }{2} }[/tex] is the critical value of  [tex]\frac{\alpha }{2}[/tex] which is obtained from the z-table.The  value is

              [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05 }{2} } = 1.96[/tex]

The reason we are obtaining critical value of    [tex]\frac{\alpha }{2}[/tex]  instead of    [tex]\alpha[/tex] is because    [tex]\alpha[/tex]

represents the area under the normal curve where the confidence level interval (   [tex]1- \alpha[/tex] ) did not cover which include both the left and right tail while  

 [tex]\frac{\alpha }{2}[/tex]  is just the area of one tail which what we required to calculate the margin of error .

NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)

So

      [tex]E = 1.96 * \sqrt{\frac{ 0.0125 (1-0.0125 )}{800} }[/tex]

     [tex]E = 0.007699[/tex]

The  95%  confidence interval is mathematically represented as

       [tex]\r p - E < p < \r p - E[/tex]

substituting values

      [tex]0.0125 - 0.007699 < p < 0.0125 + 0.007699[/tex]

      [tex]0.004801 < p < 0.020199[/tex]

Now given the p = 0.01 is within this interval then the CI  agrees with answer gotten in a

Answer:

Option (4)

Step-by-step explanation:

By the Angle of intersecting secants,

"If two lines intersect outside a circle, then the measure of the angle between these lines or secants will be one half of the difference between the intercepted arcs."

From the picture attached,

Angle between the secants = ∠1

Measure of intercepted arcs are a° and b°.

By this theorem,

m∠1 = [tex]\frac{1}{2}(a-b)[/tex]

Option (4) will be the answer.

Answer:

160 adults and 80 students

Step-by-step explanation:

With the information from the exercise we have the following system of equations:

Let x = number of students; y = number of adults

I want to maximize the following:

z = 3 * x + 6 * y

But with the following constraints

x + y = 240

y / 2 <= x

As the value is higher for adults, it is best to sell as much as possible for adults.

So let's solve the system of equations like this:

y / 2 + y = 240

3/2 * y = 240

y = 240 * 2/3

y = 160

Which means that the maximum profit is obtained when there are 160 adults and 80 students, so it is true that added to 240 and or every two adults, there must be at least one student.

Answer:

In order to solve this problem, we need to know the volume of a sphere.

The volume of a sphere is (4/3)pir^3

In this case our r value, or radius, is 30cm.

If we plug in 30cm to the equation like so:

(4/3)pi(30)^3

The answer is 113097 cm^3 of air

Hope you understand

Answer:

Step-by-step explanation:

2.8 kilometers farther. Subtract 12.1km for Winchester and 9.3 for Stamford to get 2.8 kilometers.

Answer:

converse of alternate exterior angle theorem

Step-by-step explanation:

um im not sure if i should explain the full proof but

Answer:

what we have to tell

Step-by-step explanation:

please send the correct information

Answer:

The answer on PLATO is Graph Z.

Step-by-step explanation:

I just had this question and got it right!!!

Hope this Helps!!!

Answer: What is the question to this?

Step-by-step explanation: thank you have a good day yup yup