Find the recursive formula for this general term formula. [tex]t_{n} = n!/9^{-(n-1)}, n\geq 3[/tex]

Complete Question

The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 100 hours. A random sample of 64 light bulbs indicated a sample mean life of 350 hours

A. Construct a 95% confidence interval estimate for the population mean life of light bulbs in this shipment.

B. Do you think that the manufacturer has the right to state that the light bulbs have a mean life of 400

a. No.

b. Yes.

c. Maybe.

d. Do not know

Answer:

A

   [tex]325.5 < \mu < 374.5[/tex]

B

  correct option is  a

Step-by-step explanation:

From the question we are told that

   The  standard deviation is  [tex]\sigma = 100[/tex]

    The  sample mean is  [tex]\= x = 350 \ hours[/tex]

      The sample  size is  [tex]n = 64[/tex]

Given that the confidence level is  95%  then the level of significance is mathematically represented as

            [tex]\alpha = (100- 95)\%[/tex]

            [tex]\alpha = 0.05[/tex]

The critical value  of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table  is  

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

Generally the margin of error is mathematically represented as

       [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

=>     [tex]E = 1.96 * \frac{100 }{\sqrt{64} }[/tex]

=>    [tex]E = 24 .5[/tex]

Generally the 95% confidence interval is mathematically represented as

     [tex]\= x - E < \mu < \= x + E[/tex]

     [tex]350 - 24.5 < \mu < 350 + 24.5[/tex]

     [tex]325.5 < \mu < 374.5[/tex]

This 95% confidence interval  can be interpreted as follows

   There is 95 confidence that the true population mean lies in this interval

 Now  looking at the interval we see that it dose not contain 400 hence

the correct answer is  No the   manufacturer do not  have  the right to state that the light bulbs last on average 400 hours

Answer:

From the given information, the value of a is 3 and the measurement of ∠R is 25°

Step-by-step explanation:

For this problem, we have to find the value of a and the measurement of ∠R. We are given some information already in the problem.

ΔJKL ≅ ΔPQR

This means that all of the angles and all of the sides of each triangle are going to be equal to each other.

So, knowing this, let;s find the measurement of ∠R first.

All triangles have a total measurement of 180°. We are already given two angle measurements. We are given that the m∠P is 90° because the small box in the triangle represents a right angle and right angles equal 90°. We are also given that the m∠Q is 65° because ∠Q is equal to ∠K so they have the same measurement. Now, let's set up our equation.

65 + 90 + m∠R = 180

Add 65 to 90.

155 + m∠R = 180

Subtract 155 from 180.

m∠R = 25°

So, the measurement of ∠R is 25°.

Now let's find the value of a.

KL is equal to PQ so we will set up an equation where they are equal to each other.

7a - 10 = 11

Add 10 to 11.

7a = 21

Divide 7 by 21.

a = 3

So, the value of a is 3.

Answer:

The number of duck is 32.

Step-by-step explanation:

Let x represent the number of rabbits.

Let y represent the number of ducks

From the question given:

The sum of rabbit and duck is 36 i.e

x + y = 36 .... (1)

The sum of the feets of the rabbit and duck is 80.

Rabbits has 4 legs

Duck has 2 legs

Therefore, the sum their feets (i.e 80) can be written as:

4x + 2y = 80 .... (2)

The equations are:

x + y = 36 .... (1)

4x + 2y = 80 .... (2)

Solving by substitution method:

From equation (1)

x + y = 36

Make x the subject

x + y = 36

x = 36 - y

Substitute the value of x into equation (2)

4x + 2y = 80

x = 36 - y

4(36 - y) + 2y = 80

Clear bracket

144 - 4y + 2y = 80

144 - 2y = 80

Collect like terms

- 2y = 80 - 144

- 2y = - 64

Divide both side by - 2

y = - 64/ - 2

y = 32

Therefore, the number of duck is 32.

Answer:

dollars per hour rate = $10

hours per dollar = 6 minutes 15 seconds

Step-by-step explanation:

Take note that one is singular (dollar) without an 's', and the other is plural (dollars). Thus, since her dollars per hour rate tells us how much she will earn for each hour of work, we would expect her hours per dollar rate to tell us how much she has to work in minutes to earn a single dollar ($1).

If we divide [tex]\frac{10}{60 minutes}[/tex] = $0.16 which indicates how much she earns for every minute she works at the theater. Further dividing this value into 1 minute we find the hour per dollar rate 1/0.16 = 6.25. minutes.

Answer:This was my answer.

If she were to earn dollars per hour, then she would get 16 cents for every minute she worked. If she were to work hours per dollar, then for every dollar, she would work 10 minutes for that dollar. If we divide 10 dollars by 60 minutes, then we would get 16 cents per minute. If we divide 60 minutes by 10 dollars, then we would get 6 minutes for each dollar.

Step-by-step explanation: This is the criteria.

Sample Response

10 dollars/hour describes how much money Mariah earns for each hour she works.

1/10  hour/dollar describes how much time Mariah has to work for each dollar she earns.

Evaluate Your Response

Your response should state and describe the two unit rates. To find hours per dollar, write the rate as 1 hour/ $10 and divide the numerator and denominator by 10.

Answer:

210cm³

Step-by-step explanation:

v=1/2bhl

v-1/2(7)(6)(10)

v=210

Answer:

23

Step-by-step explanation:

Answer:

[tex]\huge \boxed{\mathrm{4}} \\ \huge \boxed{\mathrm{2}}[/tex]

Step-by-step explanation:

Rate of change is another term for the slope.

rate of change = slope = (change in y)/(change in x)

Function A:

y = mx + b (m = slope)

y = 4x - 3

Function A has a slope of 4.

The rate of change for function A is 4.

Function B:

Take two points.

(-1, 0) and (1, 4)

slope = (y2 - y1)/(x2 - x1)

slope = (4 -0)/(1 - -1)

slope = 4/2 = 2

The rate of change for function B is 2.

Answer:

Hi! The answer would be 21.

Step-by-step explanation:

First, we must add.

[tex]15 + 14 = 29[/tex]

29 is our first number. Bailey cannot evenly split the cookies into each bag with that amount of cookies, so we must move on to the next number.

[tex]10 + 9 + 2 = 21 [/tex]

21 can be divided 3 times by 7. Now we know the least amount of cookies total, is 21.

Hope this helped!

Answer: D) how close a measured value is to the actual value.

Step-by-step explanation: Accuracy is simply a measurement metric which is used to establish how a measured or predicted value conforms to the actual measurement usually in terms of closeness. Accuracy is different from precision which measures closeness in values obtained from repeated measurement of the same sample. For instance;

If the actual vale of a measurement is : 11.34

Prediction 1 : 11.30

Prediction 2 : 11.32 ;

Prediction 2 will be said to be more accurate than prediction 1 becuase it is closer to the actual value than prediction 1.

Answer:

(4 + 7i)(4 - 7i)

Step-by-step explanation:

Factors of the form of a conjugate pair always produce a real number

(a + bi)(a - bi) ← produce a real number product ( a and b are real ), that is

(a + bi)(a - bi) ← expand using FOIL

= a² - bi² ( i² = - 1)

= a² + b² ← a real number

Thus

(4 + 7i)(4 - 7i)

= 16 - 49i²

= 16 + 49 = 65

Answer:

the correct answer is the last one, (4+7i)(4-7i)

Step-by-step explanation:

Answer:

y = 0.019x - 7

32.9 therms

0.019 therms

1.9 therms

Step-by-step explanation:

Given the following :

X =size of house (sq ft)

Y = Amount of natural gas used

The general form of a some linear regression model :

y = ßx + a

Where ;

ß = slope or gradient

x = independent variable

y = predicted value

a = y- intercept value

(A)

If ß = slope of population regression line = 0.019

a = y intercept of population regression line = -7

The regression model could be expressed as :

y = 0.019x + (-7)

y = 0.019x - 7

(B)What is the mean value of gas usage for houses with 2100 sq ft of space?

Here x = 2100 sq ft ; Inputting the value of x into the regression equation:

y = 0.019x - 7

y = 0.019(2100) - 7

y = 39.9 - 7

y = 32.9 therms

C) What is the average change in usage associated with a 1 square foot increase in size?

Change in usage associated with change in size can be gotten from :

ßx, where, ß change in y with respect to x ;

x = 1 square foot

ß = 0.019

Change = 0.019*(1) = 0.019 therms

(d) What is the average change in usage associated with a 100 square feet increase in size?

ßx, where, ß change in y with respect to x ;

x = 100 square feet

ß = 0.019

Change = 0.019*(100) = 1.9 therms

Hi there! :)

Answer:

[tex]\huge\boxed{\frac{29}{61}}[/tex]

Express the given scenario as a fraction:

[tex]\frac{58}{122}[/tex]

Simplify the fraction by taking out the GCF, or 2:

[tex]\frac{2(29)}{2(61)}[/tex]

Cancel out the 2's:

[tex]\frac{29}{61}[/tex]

Answer: 58/122 I think and if simplified I think it would be 29/61

Step-by-step explanation:

122 containers of juice would be the denominator

and 58 is orange juice would be the numerator

then you can leave it or simplify!

Answer: 1/6

Approximately the same.

Step-by-step explanation:

Answer:

The first answer was:1/6

The second answer was: approximately the same.

Step-by-step explanation:

Just did it on edge2020

Answer:

Luke saw 5 worms

Step-by-step explanation:

Evan and Luke saw 8 worms on the path.

Evan saw 3 worms while Luke saw 2 Worms more than Evan.

So luke is +2 of Evan

Luke= 3+2

Luke = 5

Luke saw a total of 5 worms while Evan saw a total of 3 worms adding up to a total of 8 worms

Answer:

The  probability is  [tex]P(I | \ L ) =0.4[/tex]

Yes with the additional information that the person logs on everyday the probability increased from  [tex]P(I) = 0.3[/tex]  to [tex]P(I | L ) = 0.4[/tex]

Step-by-step explanation:

From the question we are told that

   The probability that the user is from outside the country is  [tex]P(O) = 0.7[/tex]

    The probability that the user log on everyday is  [tex]P(L) = 0.6[/tex]

    The  probability that the user log on everyday and he/she is from inside the country  is  [tex]P(L| I) = 0.80[/tex]

Generally using Bayes theorem the the probability that a person is from the country given that he logs on the website every day is mathematically represented as

        [tex]P(I | \ L ) = \frac{ P(L|I) * P(I)}{ P(L)}[/tex]

Here [tex]P(I)[/tex] is the probability that the person log on every day and it is mathematically evaluated as

        [tex]P(I) = 1 - P(O)[/tex]

          [tex]P(I) = 1 - 0.7[/tex]

         [tex]P(I) = 0.3[/tex]

So

      [tex]P(I | \ L ) = \frac{ 0,8 * 0.3}{ 0.6}[/tex]

      [tex]P(I | \ L ) =0.4[/tex]

Answer:

This can be solved by subtracting 584 from 2,054.

2,054-584

=1470

Step-by-step explanation:

Gemma would have $1470 left in her checking account. hope this helps you :)

Answer: Hey There!!

The answer to this is: Option D. If two triangles ΔABC and ΔA'B'C' are similar then we take point C of ΔABC to find the transformation performed form C to C'.

Coordinates of C are (0, 3) and the coordinates of C' are (0, -1).

This shows that C is rotated 180° about origin to get the new coordinates as (0, -3) and then new coordinates were dilated by 1/3 which forms C' as (0, -1)

Therefore option D is the correct option.

Hope It Helped!~ ☆

ItsNobody~ ♡

Triangle ABC was rotated 180° about the origin, then a by a scale factor of 1/3 was done to form triangle A'B'C'.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Given that;

Triangle ABC is similar to A"B"C".

Now, If a point A(x, y) is rotated clockwise by 180 degrees, the new point is at A'(y, -x)

Hence, Triangle ABC was rotated 180° about the origin, then a by a scale factor of 1/3 was done to form triangle A'B'C'.

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Question options:

There is not sufficient evidence to reject the claim μ ≤ 3.6.

There is sufficient evidence to reject the claim μ ≤ 3.6.

There is sufficient evidence to support the claim μ ≤ 3.6.

There is not sufficient evidence to support the claim μ ≤ 3.6.

Answer:

There is sufficient evidence to reject the claim μ ≤ 3.6.

Step-by-step explanation:

The null and alternative hypotheses denoted H0 and Ha respectively are used in inferential statistics to test relationship between two variables.

the null hypothesis holds the default position and is the one tested while the alternative hypothesis is everything else. The alternative hypothesis can not be proven. From the above example if we wish to reject the null hypothesis which holds the default position that students study a most 3.6 hours, we reject H0, the null hypothesis which holds that position . In other words the null hypothesis is innocent until proven guilty

Answer:

15

Step-by-step explanation:

6/10=9/x

cross multiply

6x=9*10

6x=90

x=90/6x=15

Answer:

-1 (4 + (-4))

Step-by-step explanation:

Any number multiplied by 0 is equal to 0

in the first option given we should calculate inside the

parenthesis first then multiply which I will give result equal to 0

Answer:

-1[4 + (-4)]

Step-by-step explanation:

So first we need to evaluate the original expression, -1(0) = 0 since this is equivalent to saying negative one times zero is zero.

Now let's look at the options.

-1[4 + (-4)] evaluates using order of operations and the distributive property to -1[0] = 0. Notice this is the same as our original expression.

-1[4 + (4)] evaluates to -1[8] = -8. Note, this is different from the original expression.

1 + [4 + (-4)] evaluates to 1 + [0] = 1. Note this is different from the original expression.

-1[-4 + (-4)] evaluate to -1[-8] = 8. Note this is different from the original expression.

So we want to choose the first option which matches the original expression.

Cheers.

Answer:

7.41

Step-by-step explanation:

1.3 x 5.7

just use a calculator

Answer: Quadrant 1 (northeast quadrant)

=================================================

Explanation:

Add on 360 degrees to do a full rotation

-302+360 = 58

So angles -302 degrees and 58 degrees are pointing in the same direction. These angles are in quadrant 1, which is the northeast quadrant

Note: because the angles -302 and 58 point in the same direction, we consider these angles to be coterminal.

(A)

Evaluate [tex]p[/tex] and [tex]q[/tex] at the given values of [tex]t[/tex], then plug them into the inner product:

[tex]p(t)=3t-t^2\implies\begin{cases}p(-1)=-4\\p(0)=0\\p(1)=2\end{cases}[/tex]

[tex]q(t)=3+2t^2\implies\begin{cases}q(-1)=5\\q(0)=3\\q(1)=5\end{cases}[/tex]

Now,

[tex]\langle p,q\rangle=4\cdot5+0\cdot3+2\cdot5=30[/tex]

[tex]\|p\|=\sqrt{\langle p,p\rangle}=(-4)^2+0^2+2^2=20[/tex]

[tex]\|q\|=\sqrt{\langle q,q\rangle}=5^2+3^2+5^2=59[/tex]

(B)

Let [tex]V[/tex] denote the subspace spanned by [tex]p[/tex]. We need an orthonormal basis for [tex]V[/tex]. Since

[tex]p(t)=3t-t^2=3\cdot t+(-1)\cdot t^2[/tex]

we have the basis vectors [tex]\{t,t^2\}[/tex]; normalize these vectors to get the orthonormal basis,

[tex]\left\{\dfrac t{|t|},\dfrac{t^2}{|t^2|}\right\}=\left\{\dfrac t{|t|},1\right\}[/tex]

Then the projection of [tex]q[/tex] onto [tex]V[/tex] is

[tex]\mathrm{proj}_Vq(t)=\left(q(t)\cdot\dfrac t{|t|}\right)\dfrac t{|t|}+\left(q(t)\cdot1\right)1[/tex]

[tex]\mahtrm{proj}_Vq(t)=\dfrac{3t^2+2t^4}{t^2}+(3+2t^2)=\boxed{6+4t^2}[/tex]

A).

[tex]< p, q >=-10\\||p||=9\sqrt{2} \\||q||=3\sqrt{2}[/tex]

B).The orthogonal projection of q onto the subspace spanned by p is[tex]proj_vq(t)=6+4t^2[/tex]

We have [tex]p(t) = 3t - t^2 ,q(t) = 3 + 2t^2[/tex]

And < p, q >= p(−1)q(−1) + p(0)q(0) + p(1)q(1).

Now,

A).

[tex]p(-1) = 3.(-1) - (-1)^2 \\=-4\\p(1)=3.1-1^2\\=2q(-1) = 3 + 2.(-1)^2\\=5\\q(1) = 3 + 2.(1)^2\\=5p(0) = 3.0 - 0^2 \\=0\\q(0) = 3 + 2.0^2\\=3\\< p, q >= p(-1)q(-1) + p(0)q(0) + p(1)q(1)\\< p, q >=-4.5+0.3+2.5\\=-10\\||p||=<p,p>\\=\sqrt{(-4)^2+0+2^2} \\=\sqrt{20} \\=2\sqrt{5} \\||q||=<q,q>\\=\sqrt{5^2+3^2+5^2} \\=\sqrt{59}[/tex]

B)Let V be the subspace spanned by p.

Now, an orthonormal basis for p is[tex](t,t^2)[/tex]

 Then the projection of q onto the subspace spanned by p is

[tex]proj_vq(t)=(q(t).\frac{t}{|t|} ).\frac{t}{|t|} +(q(t).1)1\\proj_vq(t)=\frac{3t^2+2t^4}{t^2} +(3+2t^2)\\proj_vq(t)=6+4t^2[/tex]

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Answer:

32°

Step-by-step explanation:

90 - 58 = 32

The angle of depression from point A to point C is 32°.

The angle of depression is the angle formed by the horizontal line of sight intersecting with the line of sight down to an object. You might estimate the angle of depression if you were standing on top of a hill or a structure, gazing down at an item.

We are asked to find the angle of depression from point A to point C.

We can see the horizontal line of sight by the dotted line. We let this line be AD.

We know that AD ⊥ AB, as AD is the horizontal line of sight, and AB is also perpendicular to B (given).

∴ ∠DAB = 90°.

We can write ∠DAB = ∠DAC + ∠BAC.

or, 90° = ∠DAC + 58°

or, ∠DAC = 90° - 58° = 32°.

We know ∠DAC represents the angle of depression from point A to point C, as DA is the horizontal line of sight and AC is the line of sight to the object, and ∠DAC is between the lines DA and AC.

∴ The angle of depression from point A to point C is 32°.

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Answer:

13:20

Step-by-step explanation:

Start time:

Trip duration:

End time= ?

Simply adding up the time the family left and time in trip:

Sum of minutes:

Sum of hours:

So time arrival is:

Time they left is 09:30 and it will take 2 hr and a half before noon.

Splitting 3 hr and 50 min into two parts, one part being 2 hr and 30 min and the other is:

Adding 2 hr 30 min and then adding 1 hr 20 min to initial time of 09:30:

Then:

Answer:

Percentage profit= 33.33%

Step-by-step explanation:

Angela made $90000 income in 2004 then in 2005 she made income of $120000.

The percentage increase on her income will be determined by subtracting tge the initial profit from the final profit then dividing by the initial and multiplying by 100.

Profit= 120000-90000

Profit= 30000

Percentage profit=( 30000/90000)*100

Percentage profit= 1/3 *100

Percentage profit= 33.33%

Answer:

The answer is 33.33%

Answer:

Hey there!

He can guess in 4x4x4x4x4x4 or 4096 ways.

Let me know if this helps :)

Answer:

20 cm

Step-by-step explanation:

8/2 = 4

6/2 = 3

3 and 4 are the sides of the triangle (four triangles in rhombus)

[tex]a^{2} + b^{2} = c^{2} \\4^{2} + 3^{2} = c^{2}[/tex]

c = 5

5 x 4 = 20

Hope that helped!!! k

Answer:

y=1

Step-by-step explanation:

if x=15

y=4

now what is y when the value of x is 60.

15x4/60

15x4=60

60/60=1

y=1

The solution is : the value of y is: y=1

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here, we have,

given that,

y varies inversely with x. If x = 15 and y = 4 ,

now, we have to find y when x = 60

so, we have,

if x=15

y=4

now what is y when the value of x is 60.

15x4/60

15x4=60

60/60=1

y=1

Hence, The solution is : the value of y is: y=1

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