The diameter of a spindle in a small motor is supposed to be 5.8 millimeters (mm) with a standard deviation of 0.14 mm. If the spindle is either too small or too large, the motor will not work properly. The manufacturer measures the diameter in a sample of 12 spindles to determine whether the mean diameter has moved away from the required measurement. Suppose the sample has an average diameter of 5.88 mm. What are the null and alternative hypotheses (H0 = null hypothesis and Ha = alternative hypothesis)?
A. H0: Mean= 5 and Ha: Mean is not equal to 5.
B. H0: Mean = 5 and Ha: Mean <5.
C. H0: Mean < 5 and Ha: Mean > 5.
D. H0: Mean = 5 and Ha: Mean > 5.

Answer:

We know that:

Sin(a + b) = sin(a)*cos(b) + sin(b)*cos(a)

Then if we use this property in our expression:

sin(a-30)-sin(a+30)

We get:

sin(a)*cos(-30°) + sin(-30°)*cos(a) - sin(a)*cos(30°) - sin(30°)*cos(a)

Now remember that:

sin(-x) = -sin(x)

and

cos(-x) = cos(x)

Then we can rewrite our expression as:

sin(a)*cos(30°) - sin(30°)*cos(a) - sin(a)*cos(30°) - sin(30°)*cos(a)

= -2*sin(30°)*cos(a)

and sin(30°) = 0.5

Then:

-2*sin(30°)*cos(a) = -2*0.5*cos(a) = -cos(a)

So we get:

sin(a-30)-sin(a+30)= - cos(a)

Answer:

y = 0, -2

Step-by-step explanation:

Factor out the common term 3y.

[tex]3y( {y}^{2} + 4y + 4) = 0[/tex]

Rewrite y² + 4y + 4 in the form of a² + 2ab + b², where a = y and b = 2.

[tex]3y( {y}^{2} + 2(y)(2) + {2}^{2} ) = 0[/tex]

Use square sum: (a + b)² = a² + 2ab + b².

[tex]3y(y + 2) ^{2} = 0[/tex]

solve for y.

y = 0, -2.

therefor, the answer for this equation is 0, - 2.

Answer:

4. The strength of class V is 300

5. Meenakshi bought a TV for Rc 46,000

Step-by-step explanation:

4. To round to the nearest hundred, check the number in the 'tens'. If its five or greater, round up, and if its lower than 5, round down. In this case it was 7, so we rounded up to 300.

5. To round to the nearest thousand, check the number in the 'hundreds'. If its five or greater, round up, and if its lower than 5, round down. In this case it was 3, so we rounded down to 46,000.

Answer:

Hi! The answer is in the pic below!!

Step-by-step explanation:

☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆

☆Brainliest is greatly appreciated!☆

Hope this helps!!

- Brooklynn Deka

Answer:

the steady-state percentage of residents who are uninvolved is 0.5

Step-by-step explanation:

 Given the data in the question;

let N represent total number of people in the dormitory

I represent  people involved in a relationship

and U represent people uninvolved in a relationship.

so

N = I + U

I = N - U ------ let this be equation 1

Rate of Uninvolved = U/N

now, given that rate of break ups B = 15% every month = 0.15

rate of entering into relationship  R = 15% every month = 0.15

Now, the steady state condition is;

RU = BI ------- let this be equation 2

such that uninvolved rate is constant.

we input equation 1 into 2;

RU = B( N - U  )

we divide both sides by N

RU/N = B( N/N - U/N  )

RU/N = B( 1 - U/N  )

U/N = B / (B + R)

so we substitute

U/N = 0.15 / (0.15 + 0.15)

U/N = 0.15 / 0.3

U/N = 0.5

Therefore, the steady-state percentage of residents who are uninvolved is 0.5

Answer:

the answer is 1 because the power of any no. 0 is always 1

Answer:

1 package of dog bones = 4.875

1 package of cat treats = 2.1875

Step-by-step explanation:

you add the $1 to the 18.50 = 19.50 these are the amount of money for 4 bags of dog food. you take away all the dog food(4) from it = 8.75 divide by 4 for the 4 bags of cat food= 2.1875

sorry I'm very bad at explaining you can put it in your own words

Answer:

Not an answer but OMG

Step-by-step explanation:

I love the Whitty profile pic :)

Answer:

third side = 7

Step-by-step explanation:

x² = 9² - (4√2)² = 81 - 32 = 49

x = √49 = 7

Answer:

That's false

Step-by-step explanation:

6000(1.02)³⁶​ = 2.1 × 10¹³⁶

Answer:

hope this helps (if it does can i have brainliest, please??)

Step-by-step explanation:

I believe that is <KLJ and <MLJ

Answer:

KLJ and MLJ

Step-by-step explanation:

Supplemenatry angles add up to 180 degrees. Since these two angles form a straight line, it can be assumed that they add up to 180 degrees. Hope it helps :)

Answer:

C.

Step-by-step explanation:

Before graphing this equation we first need to isolate y on one side like so...

y + 2 = 3(x+1)   ... distribute the 3 to both values inside the parenthesis

y + 2 = 3x + 3   ... subtract 2 on both sides

y = 3x + 1

Now that we have the y variable isolated we see that the slope of the function is 3, meaning that for every 1 unit right the line needs to move 3 units up. We also have the value where the line needs to cross the y-axis and that is 1. Using this information we see that the correct graph is C.

Answer:

Heyyyyy! Help with what?

Step-by-step explanation:

Let me know :)

Have a nice day <3

Answer:

16+12i

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

Zero is Soo's miserly number. It won't give the number four

Answer:

1. right

2. acute

3. obtuse

4. obtuse

5. acute

6. acute

7. scalene

8. scalene

9. isosceles

10. equilateral

11. scalene

12. isosceles

Step-by-step explanation:

Answer:

x=y-75x-5y=-35

Step-by-step explanation:

The answer is A the y=2.25

The equation of the exponential regression that fits these data,

y = 2.25 [tex](1.75)^x[/tex]

It is a model that explains processes that increase at twice the rate. It is employed in circumstances where growth starts slowly but quickly accelerates without bounds, or decay starts quickly but slows down to zero.

The formula for expressing Exponential Regression is

y = a[tex]b^x[/tex]

We have given that,

The table below represents The closing prices of stock at TUV for the last five days

Days      Value

1           3.938

2          6.891

3          12.059

4          21.103

5          36.929

First we have to find r as

r= 6.891/ 3.938

r = 1.749

As, the standard form of Exponential function

y = a[tex]b^x[/tex]

So, y = 2.25 [tex](1.75)^x[/tex]

learn more about linear regression here:

brainly.com/question/25987747

#SPJ7

Answer:

0.0367 = 3.67% probability that exactly 6 patients will die

Step-by-step explanation:

The patients are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question, we have that:

20 patients means that [tex]N = 20[/tex]

Sample of 8 means that [tex]n = 8[/tex]

9 have the heart problem, so [tex]k = 9[/tex]

What is the probability that exactly 6 patients will die?

This is P(X = 6).

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 6) = h(6,20,8,9) = \frac{C_{9,6}*C_{11,2}}{C_{20,8}} = 0.0367[/tex]

0.0367 = 3.67% probability that exactly 6 patients will die

Answer:

59

Step-by-step explanation:

360 - ( 156 + 86 ) = 118

118 / 2 = 59

Answer: B. 12.7

Step-by-step explanation:

Answer:

D.8.5

Step-by-step explanation:

38.4/2=

19.2 L

19.2-10.7=

8.5

hope this helps ; )

Answer:

B

Step-by-step explanation:

Marcus can expect to have red chip 20 times.

Probability denotes the possibility of the outcome of any random event. The meaning of this term is to check the extent to which any event is likely to happen.

Given that, Marcus has a bag of 10 red chips, 15 blue chips, and 5 black chips.

He did an experiment 60 times and we need to find that how many times would he expect to pick a red chip,

So,

Here the favorable outcomes = red chips (10)

Total outcomes = all the chips = 15+5+10 = 20

So, the probability of finding a red chips for the 60 times = 10/20 x 60

= 30

Hence, Marcus can expect to have red chip 20 times.

Learn more about probability, click;

https://brainly.com/question/30034780

#SPJ2

Answer:

B

Step-by-step explanation:

Remark

I'm hesitant to get an exact answer. You could do that with the cos law for distance. To get an approximate answer you could use the Pythagorean Theorem.

I'll try the cos law first.

Formula

c^2 = a^2 + b^2 - 2abcos(C)

Givens

c = 24

a = 18

b = ?

Solution

24^2 = 18^2 + b^2 - 2*18*b*cos(94)

576 = 324 + b^2 - 36*b*(-0.0698)

0 = 324 - 576 + b^2 + 2.511b

0 = b^2 + 2.511 - 252

Using the quadratic formula, the roots are

b1 = 14.66

b2 = - 17.11

The second one has no meaning in the real world.

Answer

the distance is 14.66 miles from Chaplin to Asherville

Note: using the Pythagorean theorem gives 15.87 which I would count as a good approximation.

Answer:

14.7

Step-by-step explanation:

got 100% on plato

Answer:

$258.75

Step-by-step explanation:

225 * 0.15

Let last weeks pay = x

This week she earned 15% more so she earned 100% + 15% more for 115% total.

Setup an equation:

115% times x = $225

115% as a decimal = 1.15

So the equation is:

1.15x = 225

Solve for x by dividing both sides by 1.15:

X = 225/1.15

X = 195.65

Last week she earned $195.65

Answer:

If 34.54 is the diameter then 17.27 is the radius

Step-by-step explanation:

34.54 ÷ 2 = 17.27

Answer:

I love algebra anyways  

the ans is in the picture with the steps  

(hope it helps can i plz have brainlist :D hehe)

Step-by-step explanation:

Answer:

1750

Step-by-step explanation:

So first we have to find out how much tax he pays which is 30% of 2,500=750. now we know how much tax he pays, we can subtract it from his salary: 2500-750=1750

Answer:

4

Step-by-step explanation:

Another way to write this is 8/1 x 1/2. Then the answer would be 8/2. Simplify to get 4.

8 × 1/2 = 4!

Calculation steps:

8 ×

1

2

= 8 ×

1

2

=

8 × 1

1 × 2

=

8

2

=

8 ÷ 2

2 ÷ 2

= 4