Give the null and alternative hypotheses in symbolic form that would be used in a hypothesis test of the following claim:
The mean time between "clicks" of the second hand on a particular clock is not 1 second.
a. H0: = 1 vs. H1: 1
b. H0: p = 1 vs. H1: p 1
c. H0: = 1 vs. H1:
d. none of these

Answer:

The Taylor series is   [tex]$$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]

Step-by-step explanation:

From the question we are told that

      The function is  [tex]f(x) = sin (x)[/tex]

This is centered at  

       [tex]a = 2 \pi[/tex]

Now the next step is to represent the function sin (x) in it Maclaurin series form which is  

          [tex]sin (x) = \frac{x^3}{3! } + \frac{x^5}{5!} - \frac{x^7}{7 !} +***[/tex]

=>       [tex]sin (x) = $$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]

   Now since the function is centered at  [tex]a = 2 \pi[/tex]

We have that

           [tex]sin (x - 2 \pi ) = (x-2 \pi ) - \frac{(x - 2 \pi)^3 }{3 \ !} + \frac{(x - 2 \pi)^5 }{5 \ !} - \frac{(x - 2 \pi)^7 }{7 \ !} + ***[/tex]

This above equation is generated because the function is not centered at the origin but at [tex]a = 2 \pi[/tex]

           [tex]sin (x-2 \pi ) = $$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x - 2 \pi)^{2n+1}][/tex]

Now due to the fact that [tex]sin (x- 2 \pi) = sin (x)[/tex]

This because  [tex]2 \pi[/tex] is a constant

   Then it implies that the Taylor series of the function centered at [tex]a = 2 \pi[/tex] is

             [tex]$$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]

Answer:

Step-by-step explanation:

[tex]\frac{x-1}{2} =t\\\frac{y-2}{3} =t\\\frac{z-3}{4} =t\\so~eq.~of~line~L_{1}~is\\\frac{x-1}{2} =\frac{y-2}{3} =\frac{z-3}{4} \\its~d.r's~are~2,3,4\\again~\frac{x-2}{1} =s\\\frac{y-4}{2} =s\\\frac{z+1}{-4} =s\\so~eq. ~of~line~L_{2}~is\\\frac{x-2}{1} =\frac{y-4}{2} =\frac{z+1}{-4} \\its~d.r's ~are~1,2,-4\\let ~the ~d.r's~of~line~perpendicular~to~both~L_{1}~and~L_{2}~be~a,b,c,~then~\\2a+3b+4c=0\\1a+2b-4c=0\\solving\\\frac{a}{3*-4-4*2} =\frac{b}{4*1-2*-4} =\frac{c}{2*2-3*1} \\[/tex]

[tex]\frac{a}{-20} =\frac{b}{-4} =\frac{c}{1} \\d.r's~of ~reqd~line~is~-20,-4,1~or~20,4,-1[/tex]

now you find the point of intersection.

then calculate the angle.

Answer:

(-2,-110)

Step-by-step explanation:

First solve for x

20x−70=70x+30

x= -2

Now substitute x for -2

y=20x−70

y=20(-2)-70

y = -110

Answer:

Hi! Answer will be below.

Step-by-step explanation:

The answer is 450.

If you divide 1.8 and 0.004 the answer you should get is 450.

Below I attached a picture of how to do long division...the picture is an example.

Hope this helps!:)

⭐️Have a wonderful day!⭐️

Answer:

10 miles

Step-by-step explanation:

3 mi/1 hr  x (h hours + 2/3 hr) = 5 mi/1 hr  x  h hours

3h + 2 = 5h

2 = 2h

h = 1 hour

3mi/hr  x 1 2/3 hr = 5 miles

5 mi/hr x  1 hr = 5 miles

He hiked 10 miles. (

Answer:

B. The problem involves a combination because the order in which the letters are selected does not matter.

Step-by-step explanation:

Computation technique is a method of statistics to find possible ways of combination. In computation technique it is assumed that order does not matter and letters will be selected at random. Permutation is a statistics technique to find possible ways of combination when the order does matter. Permutation technique cannot be used when order does not matter.

Answer:

The answer is:

The fourth option,

{s | s <90}

Step-by-step explanation:

yes

Answer:

[tex]\boxed{s|s<90}[/tex]

Step-by-step explanation:

1/3s-6<24

Add 6 on both sides.

1/3s<30

Multiply both sides by 3.

s<90

Answer:

The answer is option B.

Step-by-step explanation:

six less than a number is written as

x - 6

Hope this helps you

Answer:

0.29

Step-by-step explanation:

There are 29 squares shaded in. In all, there are 100 squares in the 10 × 10 square, so there are 29 shaded squares out of 100 squares in all. That is basically:

[tex]\frac{29}{100}[/tex]

[tex]\frac{29}{100}[/tex] can be converted to 0.29.

Answer:

0.29

Step-by-step explanation:

Since the grid is a 10x10, it means there are 100 total 'blocks' in the grid. So, since there are 29 shaded in out of the 100 'blocks total, the decimal would be .29, since the decimal means 29 hundredths, and it also means that there is 29 hundredths of the total grid shaded in.

Answer:

The answer is option 2.

Step-by-step explanation:

You have to apply Cosine Rule, cosθ = adjacent/hypotenuse. Then, you have to substitute the values into the formula :

[tex]cos(θ) = \frac{adj.}{hypo.} [/tex]

[tex]let \: θ = 55[/tex]

[tex]let \: adj. = 11[/tex]

[tex]let \: hypo. = x[/tex]

[tex]cos(55) = \frac{11}{x} [/tex]

The correct trigonometry formula to use to solve for x is [tex]\frac{11}{x}[/tex] . Thus option 1 is correct.

According to the question, we have

base = 11

hypotenuse = x

here for [tex]cos Ф[/tex]Ф,  it is not required to find the value of perpendicular,

we know that in a right-angle triangle using trigonometric ratio, we get

[tex]cos Ф[/tex] Ф = [tex]\frac{base }{hypotenuse}[/tex]

[tex]cos Ф[/tex] Ф = [tex]\frac{11}{x}[/tex]  

here  Ф = [tex]55 ^0[/tex]

[tex]cos 55^o = \frac{11}{x}[/tex]

Thus, the value of the trigonometry formula to use to solve for x is  [tex]\frac{11}{x}[/tex].

Thus option 1 is correct.

Learn more about Trigonometry here :

https://brainly.com/question/22986150

#SPJ2

Answer:

3/26

Step-by-step explanation:

Probability of the first box to have the secret decoder ring is 18 out of 52:

Probability of the second box to have the ring is 17 out of 51, because one box with the ring already selected and not counted:

Probability that both of them have the secret decoder ring:

So the answer is 3/26

Answer:

7987.1569 to the nearest thousandths is 7987.157

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

You have to find the vertical of x. To the right of the vertical, we see that there is an angle of 25 (since the 25 up top corresponds to that blank angle). Once you add 25 + 85 + x = 180 (since this is a straight line), we see that x is 70, and its vertical is also 70.

Answer:

[tex](4,7)[/tex]

Step-by-step explanation:

Given

[tex]2x - 3 < y[/tex]

[tex](x,7)[/tex]

Required

Find one possible value of x

From the given parameters;

[tex](x,7)[/tex] is a possible solution of [tex]2x - 3 < y[/tex] where y= 7

Substitute 7 for y

[tex]2x - 3 < 7[/tex]

Add 3 to both sides

[tex]2x - 3 + 3 < 7 + 3[/tex]

[tex]2x < 10[/tex]

Divide both sides by 2

[tex]2x/2 < 10/2[/tex]

[tex]x < 5[/tex]

The result of the inequality implies that x is less than 5; So, the possible values of x is all real numbers less than 5;

Having said that;

[tex](4,7)[/tex] is one possible coordinate of [tex]2x - 3 < y[/tex]

Answer:

x is approximately 53°

Answer:52.64°

Step-by-step explanation:

opp=31

hyp=39

sin x° =[tex]\frac{opp}{hyp}[/tex]

sin x°=31/39

sin x°=0.7949

x=[tex]sin^{-1} (0.7949)\\[/tex]

x=52.64

Answer:

U = 17 1/7

T = 51 3/7

S = 61 3/7

Step-by-step explanation:

Given

T+S+U=130\

T=3(U)

S= T+10 we have to find value of u

First step:

find S and T in terms of U

T is given

T = 3U

S = T +10 , using T = 3U

S = 3U+10

Using the above value in T+S+U=130

3U + 3U+10 + U = 130

=> 7U = 130-10 = 120

=> U = 120/7 = 17 1/7

T = 3U = 3*120/7 = 360/7 = 51 3/7

S = T+10 = 360/7 + 10 = (360+70)/7 = 430/7 = 61 3/7

Thus,

U = 17 1/7

T = 51 3/7

S = 61 3/7

Answer:

Vertical angles are congruent.

Step-by-step explanation:

Vertical angles are opposite angles formed by intersecting lines, and are always congruent.

Answer:

Larger force= 66.28 pounds

Step-by-step explanation:

The angle of the resultant force 80 pounds = 180-(52+20)

The angle of the resultant force 80 pounds = 180-72

The angle of the resultant force 80 pounds = 108°

The larger force is the force with 52°

Let the larger force be x

Magnitude of the larger force

x/sin52 = 80/sin108

X= sin52 *(80/sin 108)

X= 0.7880*(80/0.9511)

X = 0.7780*(84.1131)

X = 66.28 pounds

Answer:

The answer is #3 which is 24%.

Step-by-step explanation:

6 × 100

25

25 into 100 is 4, then 6×4 = 24%

I really hope this helps :)

Answer:

The answer is 29 unit.

Step-by-step explanation:

Here,

given that,

DC (l) =4z+1

CD (b)=5z+2

perimeter (p)= 132

now,

perimeter of rectangle (p) is= 2(l+b)

or, 132 = 2×{(4z+1)+(5z+2)}

or, 132= 2×(9z+3)

or, 132= 18z+6

or, 18z=132-6

or, z=126/18

or, z= 7.

therefore, 4z+1=4×7+1=29

5z+2= 5×7+2=37.

As our question is about to find AB,

DC = AB. (as opposite side of rectangle is equal).

so, the valueof AB is 29unit.

Hope it helps...

Answer:

a)   x₁ = 14

     x₂ = - 6

b) x = 4

c) P(max ) = 4000000 $

Step-by-step explanation:

To find the axis of symmetry we solve the equation

a) -4x² + 32x + 336 = 0

4x²  - 32x  - 336  = 0       or    x² - 8x - 84 = 0

x₁,₂ = [ -b ± √b² -4ac ]/2a

x₁,₂ = [ 8  ±√(64) + 336 ]/2

x₁,₂ = [ 8  ± √400 ]/2

x₁,₂ =( 8 ± 20 )/2

x₁  = 14

x₂ = -6

a) Axis of symmetry must go through the middle point between the roots

x = 4 is the axis of symmetry

c) P = -4x² + 32x + 336

Taking derivatives on both sides of the equation we get

P´(x) = - 8x + 32  ⇒  P´(x) = 0     - 8x + 32

x = 32/8

x = 4    Company has to sell  4 ( 4000 snowboard)

to get  a profit :

P = - 4*(4)² + 32*(4) + 336

P(max) = -64  + 128 + 336

P(max) = 400           or  400* 10000 =  4000000

Answer:

Step-by-step explanation:

Simplify each term.

y ≤ −2x/5 + 2

Find the slope and the y-intercept for the boundary line.

Slope: -2/5

Y-intercept: 2

Graph a solid line, then shade the area below the boundary line since

y is less than -2x/5 + 2

y ≤ −2x/5 + 2

Hope this can help

Answer:

Two possible sets of answers.

5 men, 11 women and 42 children, or

10 men, 2 women and 88 children

Selamat Sadhya!

Step-by-step explanation:

M = number of men

W = number of women

100-M-W = number of children

Total number of pappadas

5M+3W+(100-M-W)/2 = 100

Solve for W

W = (100-9M)/5 .......................(1)

Examine equation (1).

In order to have W as a whole number, M must be multiple of 5

Therefore M = 5 or 10

If M = 5, W = (100-45)/5 = 11 and children = 100-5-11 =  84

If M = 10, W = (100-90)/5 = 2 and children = 100-10-2 = 88

Answer:

3051.08 cm squared

Step-by-step explanation:

The equation to find lateral surface area of a cone:

SA = pi r sqrt(h^2 * r^2)

Plug your values in.

SA = 3.14 * 9 * sqrt(144*81)

SA = 3.14 * 9 * 108

SA = 3051.08

The lateral surface area is 3051.08 cm squared.

Answer:

424.12cm^2

Step-by-step explanation:

make sure you have the radius, half of the diameter!

remember to use this formula! Lateral surface area = πrs = πr√(r2 + h2)

hope this helped!

r=radius

h=hight

s=slant

Answer:

The  correct option is d

Step-by-step explanation:

From the question we are told that

    The  population size is  [tex]N = 47000[/tex]

    The  sample size is  [tex]n = 200[/tex]

     The  sample mean is   [tex]\= x = 118.0 \ mmHg[/tex]

     The  standard deviation is  [tex]\sigma = 11.0 \ mmHg[/tex]

Given that the confidence level is  95% then the level of significance can be calculated as

                     [tex]\alpha = 100 - 95[/tex]

                    [tex]\alpha = 5 \%[/tex]

                      [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from  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)

  Generally the margin of error is mathematically represented as

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

substituting values

           [tex]E = 1.96 *\frac{11.0 }{ \sqrt{200} }[/tex]

           [tex]E = 1.5245[/tex]

The  95% confidence level interval is mathematically represented as

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

substituting values

       [tex]118.0 - 1.5245 < \mu < 118.0 + 1.5245[/tex]

        [tex]116.5< \mu < 119.5[/tex]

         [tex][116.5 , 119.5][/tex]

The lowest common denominator is lcm(5, 3), which is 15.

The sum of 2/5 + 5/3 + 9/3 is 6/15 + 25/15 + 45/15, which is 76/15 or [tex]5\frac{1}{15}[/tex].

Answer:

We have sinθ = 12/13

The  method here is to figure out the value of θ

Using a calculator sin^(-1)(12/13) =67.38°

67.38° is in quadrant 1  so we must substract 67.38° from 180° wich is π

Now time to calculate cos2θ and cosθ using a calculator

The values we got make sense since θ is in quadrant 2 and 2θ in quadrant 3

Answer:

3x

Step-by-step explanation:

18 x^2 / 6x

Divide the numbers

18/6 =3

Then divide the variables

x^2 /x = x

The result is 3x

Answer:

3x

Step-by-step explanation:

18x^2/6x

x^2 / x is x

18x/6

18/6 is 3

it all simplifies into 3x

Answer:

f(x) = 500(2)^x

Step-by-step explanation:

Let's assume the initial x value is 0

500(0)^2 = 0

100(0)^5 = 0

500(2)^0 = 500

500(0)^2 = 0

Answer:

C

Step-by-step explanation:

Edge

Answer:

h = -9

Step-by-step explanation:

5h+2(11-h)= -5

Distribute

5h +22 -2h = -5

Combine like terms

3h +22 = -5

Subtract 22 from each side

3h +22-22 = -5-22

3h = -27

Divide by 3

3h/3 = -27/3

h = -9