The true average diameter of ball bearings of a certain type is supposed to be 0.5 in. A one-sample t test will be carried out to see whether this is the case. What conclusion is appropriate in each of the following situations?
(a) n = 15, t = 1.66, a = 0.05
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(b) n = 15, t = 1.66, a = 0.05
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(c) n = 26, t = 2.55, a = 0.01
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(d) n = 26, t = 3.95
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answer:

the probability that the company's total hospital costs in a year are less than 50,000  = 0.7828

Step-by-step explanation:

From the given information:

the probability that the company's total hospital costs in a year are less than 50,000 will be the sum of the probability of the employees admitted.

If anyone is admitted to the hospital, they have [tex]\dfrac{1}{3}[/tex] probability of making at least one more visit, and a [tex]\dfrac{2}{3}[/tex]  probability  that this is their last visit.

If zero employee was admitted ;

Then:

Probability = (0.80)⁵

Probability = 0.3277

If one employee is admitted once;

Probability = [tex](0.80)^4 \times (0.20)^1 \times (^5_1) \times (\dfrac{2}{3})[/tex]

Probability = [tex](0.80)^4 \times (0.20)^1 \times (\dfrac{5!}{(5-1)!}) \times (\dfrac{2}{3})[/tex]

Probability = 0.2731

If one employee is admitted twice

Probability = [tex](0.80)^3 \times (0.20)^2 \times (^5_2) \times (\dfrac{2}{3})^2[/tex]

Probability = [tex](0.80)^3 \times (0.20)^2 \times (\dfrac{5!}{(5-2)!}) \times (\dfrac{2}{3})^2[/tex]

Probability = 0.1820

If two employees are admitted once

Probability = [tex](0.80)^4\times (0.20)^1 \times (^5_1) \times (\dfrac{1}{3}) \times (\dfrac{2}{3})[/tex]

Probability = [tex](0.80)^4 \times (0.20)^1 \times (\dfrac{5!}{(5-1)!}) \times (\dfrac{1}{3}) \times (\dfrac{2}{3})[/tex]

Probability = 0.0910

∴

the probability that the company's total hospital costs in a year are less than 50,000  = 0.3277 + 0.2731 + 0.1820

the probability that the company's total hospital costs in a year are less than 50,000  = 0.7828

You want to end up with [tex]A\sin(\omega t+\phi)[/tex]. Expand this using the angle sum identity for sine:

[tex]A\sin(\omega t+\phi)=A\sin(\omega t)\cos\phi+A\cos(\omega t)\sin\phi[/tex]

We want this to line up with [tex]2\sin(4\pi t)+5\cos(4\pi t)[/tex]. Right away, we know [tex]\omega=4\pi[/tex].

We also need to have

[tex]\begin{cases}A\cos\phi=2\\A\sin\phi=5\end{cases}[/tex]

Recall that [tex]\sin^2x+\cos^2x=1[/tex] for all [tex]x[/tex]; this means

[tex](A\cos\phi)^2+(A\sin\phi)^2=2^2+5^2\implies A^2=29\implies A=\sqrt{29}[/tex]

Then

[tex]\begin{cases}\cos\phi=\frac2{\sqrt{29}}\\\sin\phi=\frac5{\sqrt{29}}\end{cases}\implies\tan\phi=\dfrac{\sin\phi}{\cos\phi}=\dfrac52\implies\phi=\tan^{-1}\left(\dfrac52\right)[/tex]

So we end up with

[tex]2\sin(4\pi t)+5\cos(4\pi t)=\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)[/tex]

Answer:

Step-by-step explanation:

In the form ...

  y(t) = Asin(ωt +φ)

you have ...

The translation from ...

  y(t) = 2sin(4πt) +5cos(4πt)

is ...

  A = √(2² +5²) = √29 . . . . the amplitude

  ω = 4π . . . . the angular frequency in radians per second

  φ = arctan(5/2) ≈ 1.1903 . . . . radians phase shift

Then, ...

  y(t) = √29·sin(4πt +1.1903)

_____

Comment on the conversion

You will notice we used "2" and "5" to find the amplitude and phase shift. In the generic case, these are "coefficient of sin( )" and "coefficient of cos( )". When determining phase shift, pay attention to whether your calculator is giving you degrees or radians. (Set the mode to what you want.)

If you have a negative coefficient for sin( ), you will need to add 180° (π radians) to the phase shift value given by the arctan( ) function.

7km/ 4km per hour = 1 3/4 hours

3/4 hour = 45 minutes

Total time = 1 hour and 45 minutes.

Answer: The length of the line B'C" is 1 unit.

Step-by-step explanation:

Given: Triangle ABC is dilated by a scale factor of 0.5 with the origin as the center of dilation , resulting in the image Triangle A'B'C'.

If A (2,2), B= (4,3) and C=(6,3).

Distance between (a,b) and (c,d): [tex]D=\sqrt{(d-b)^2+(c-b)^2}[/tex]

Then, BC [tex]=\sqrt{(3-3)^2+(6-4)^2}[/tex]

[tex]\\\\=\sqrt{0+2^2}\\\\=\sqrt{4}\\\\=2\text{ units}[/tex]

Length of image = scale factor x length in original figure

B'C' = 0.5 × BC

= 0.5 × 2

= 1 unit

Hence, the length of the line B'C" is 1 unit.

Answer:

4.24m³

Step-by-step explanation:

The inside diameter of 1.2 m of the pipe

Radius of the inside pipe = Diameter/2 = 1.2/2 = 0.6m

The outside diameter of 1.8 m

Radius of the outer of the pipe = 1.8/2 = 0.9m

Height of the pipe = 3.0m

A Pipe looks like the shape of the cylinder. Hence,

Volume of concrete in the pipe = Volume of the outer section of the Pipe - Volume of the inner section of the pipe

Volume of the outer section of the Pipe = πr²h

h = 3.0m

r = 0.9

= π × 0.9² × 3.0

= 7.63m³

Volume of the inner section of the Pipe = πr²h

h = 3.0m

r = 0.6

= π × 0.6² × 3.0

= 3.39m³

Volume of concrete in the pipe = Volume of the outer section of the Pipe - Volume of the inner section of the pipe

= 7.63m³ - 3.39m³

= 4.24m³

Therefore, volume of concrete in the pipe is 4.24m³

Answer:

(0,-2)

Step-by-step explanation:

The y-intercept is simply when the function touches or crosses the y-axis.

We're told that the graph crosses the y-axis at -2. In other words, the y-intercept is at -2.

The ordered pair would be (0,-2)

Answer:

Option B

an increasing exponential graph

Answer:

It is unlikely.

Step-by-step explanation:

Certain = 100%

Impossible = 0%

Likely = more than 50%

Unlikely = less than 50%

It is less than 50%, so it is unlikely.

Answer:

(A) it is likely

Step-by-step explanation:

i took the test on edge

Answer:

dI/dt = 0.0001(2000 - I)I

I(0) = 20

[tex]I(t)=\frac{2000}{1+99e^{-0.2t}}[/tex]

Step-by-step explanation:

It is given in the question that the rate of spread of the disease is proportional to the product of the non infected and the infected population.

Also given I(t) is the number of the infected individual at a time t.

[tex]\frac{dI}{dt}\propto \textup{ the product of the infected and the non infected populations}[/tex]

Given total population is 2000. So the non infected population = 2000 - I.

[tex]\frac{dI}{dt}\propto (2000-I)I\\\frac{dI}{dt}=k (2000-I)I, \ \textup{ k is proportionality constant.}\\\textup{Since}\ k = 0.0001\\ \therefore \frac{dI}{dt}=0.0001 (2000-I)I[/tex]

Now, I(0) is the number of infected persons at time t = 0.

So, I(0) = 1% of 2000

            = 20

Now, we have dI/dt = 0.0001(2000 - I)I  and  I(0) = 20

[tex]\frac{dI}{dt}=0.0001(2000-I)I\\\frac{dI}{(2000-I)I}=0.0001 dt\\\left ( \frac{1}{2000I}-\frac{1}{2000(I-2000)} \right )dI=0.0001dt\\\frac{dI}{2000I}-\frac{dI}{2000(I-2000)}=0.0001dt\\\textup{Integrating we get},\\\frac{lnI}{2000}-\frac{ln(I-2000)}{2000}=0.0001t+k \ \ \ (k \text{ is constant})\\ln\left ( \frac{I}{I-222} \right )=0.2t+2000k[/tex]

[tex]\frac{I}{I-2000}=Ae^{0.2t}\\\frac{I-2000}{I}=Be^{-0.2t}\\\frac{2000}{I}=1-Be^{-0.2t}\\I(t)=\frac{2000}{1-Be^{-0.2t}}\textup{Now we have}, I(0)=20\\\frac{2000}{1-B}=20\\\frac{100}{1-B}=1\\B=-99\\ \therefore I(t)=\frac{2000}{1+99e^{-0.2t}}[/tex]

The required expressions are presented below:

[tex]\frac{dI}{dt} = 0.0001\cdot I\cdot (2000-I)[/tex] [tex]\blacksquare[/tex]

[tex]I(0) = \frac{1}{100}[/tex] [tex]\blacksquare[/tex]

[tex]I(t) = \frac{20\cdot e^{\frac{t}{5} }}{1+20\cdot e^{\frac{t}{5} }}[/tex] [tex]\blacksquare[/tex]

After reading the statement, we obtain the following differential equation:

[tex]\frac{dI}{dt} = k\cdot I\cdot (n-I)[/tex] (1)

Where:

Then, we solve the expression by variable separation and partial fraction integration:

[tex]\frac{1}{k} \int {\frac{dI}{I\cdot (n-I)} } = \int {dt}[/tex]

[tex]\frac{1}{k\cdot n} \int {\frac{dl}{l} } + \frac{1}{kn}\int {\frac{dI}{n-I} } = \int {dt}[/tex]

[tex]\frac{1}{k\cdot n} \cdot \ln |I| -\frac{1}{k\cdot n}\cdot \ln|n-I| = t + C[/tex]

[tex]\frac{1}{k\cdot n}\cdot \ln \left|\frac{I}{n-I} \right| = C\cdot e^{k\cdot n \cdot t}[/tex]

[tex]I(t) = \frac{n\cdot C\cdot e^{k\cdot n\cdot t}}{1+C\cdot e^{k\cdot n \cdot t}}[/tex], where [tex]C = \frac{I_{o}}{n}[/tex] (2, 3)

Note - Please notice that [tex]I_{o}[/tex] is the initial infected population.

If we know that [tex]n = 2000[/tex], [tex]k = 0.0001[/tex] and [tex]I_{o} = 20[/tex], then we have the following set of expressions:

[tex]\frac{dI}{dt} = 0.0001\cdot I\cdot (2000-I)[/tex] [tex]\blacksquare[/tex]

[tex]I(0) = \frac{1}{100}[/tex] [tex]\blacksquare[/tex]

[tex]I(t) = \frac{20\cdot e^{\frac{t}{5} }}{1+20\cdot e^{\frac{t}{5} }}[/tex] [tex]\blacksquare[/tex]

To learn more on differential equations, we kindly invite to check this verified question: https://brainly.com/question/1164377

Answer:

  54

Step-by-step explanation:

x is half the difference of the two arcs:

  x = (136 -28)/2 = 54

The value of x is 54.

Answer:

n = 17

Step-by-step explanation:

Assuming

- probability of success (making free throw) does not vary

We have

n = 17 (trials)

p = 0.479

x > 9

The answer is "[tex]\bold{p(x>9)=0.2550319}[/tex]"

[tex]\to X:[/tex] Number of creating free throws in a set [tex]\bold{17\ \ x \sim bin(17,0.479)}[/tex]

Know we calculating the P(makes more than 9 of them)

[tex]=\bold{9(X>9)=1-P(Z<=9)}[/tex]

Using the R-code:

[tex]\to \bold{1-p\ binom(9,17,0.479)}\\\\\to \bold{[1]0.2550319}\\\\\bold{\therefore}\\\\ \to \bold{p(x>9)=0.2550319}[/tex]

Learn more:

binomial distribution: brainly.com/question/9065292

Answer:

7y⁴- 10yz - y²z - 5

Step-by-step explanation:

First collect like terms

3y²+ 4y²- 6yz - 4yz - y²z - 7+2

7y⁴-10yz - y²z - 5

Answer:

Its C

Step-by-step explanation:

the bag is 200g

total weight with oranges is 1400g

deduct the bags weight from total weight

1400 - 200

1200g

this is the weight of the three oranges

so each orange would be

1200 ÷ 3

400g

Answer: Price-earnings ratio= 22.0

Step-by-step explanation:

Given: A company had a market price of $38.50 per share, earnings per share of $1.75, and dividends per share of $0.90

To find: price-earnings ratio

Required formula: [tex]\text{price-earnings ratio }=\dfrac{\text{ Market Price per Share}}{\text{Earnings Per Share}}[/tex]

Then, Price-earnings ratio = [tex]\dfrac{\$38.50}{\$1.75}[/tex]

⇒Price-earnings ratio = [tex]\dfrac{22}{1}[/tex]

Hence, the price-earnings ratio= 22.0

Answer: 3

Step-by-step explanation:

7x=21 21/7=3

Answer:

i think (d) one i think it will help you

Answer:

B. The fact that two variables are strongly correlated does not in itself imply a​ cause-and-effect relationship between the variables.

Step-by-step explanation:

The term "correlation does not imply causation", simply means that because we can deduce a link between two factors or sets of data, it does not necessarily prove that there is a cause-and-effect relationship between the two variables. In some cases, there could indeed be a cause-and-effect relationship but it cannot be said for certain that this would always be the case.

While correlation shows the linear relationship between two things, causation implies that an event occurs because of another event. So the phrase is actually saying that because two factors are related, it does not mean that it is as a result of a causal factor. It could simply be a coincidence. This occurs because of our effort to seek an explanation for the occurrence of certain events.

Answer: B. The fact that two variables are strongly correlated does not in itself imply a​ cause-and-effect relationship between the variables.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The perimeter of a rectangle is expressed as 2(L+B) where;

L is the length and B is the breadth of the triangle.

P = 2(L+B)

68 = 2(L+B)

L+B = 68/2

L+B = 34

L = 34 - B ... 1

Area of the rectangle A = LB... 2

Substituting equation 1 into 2 will give;

A = (34-B)B

A = 34B-B²

To maximize the area of the triangle, dA/dB must be equal to zero i.e

dA/dB = 0

dA/dB = 34 - 2B = 0

34-2B = 0

2B = 34

Dividing both sides of the equation by 2 we will have;

B = 34/2

B = 17

Substituting B = 17 into equation 1 to get the length L

L = 34-17

L = 17m

This shows that the rectangle with maximum area is a square since L = B = 17m

The dimension of the rectangle is Length = 17m and Breadth = 17m

The dimensions are 17m and 17m.

The perimeter of a rectangle is given as:

= 2(length + width)

Since in their case, the lengths have same values, this will be:

Perimeter = 2(l + l)

Perimeter = 4l

4l = 68

L = 68/4

L = 17m

Therefore, the dimensions are 17m and 17m.

Read related link on:

https://brainly.com/question/15366172

Answer:

Hope this is correct

HAVE A GOOD DAY!

Answer:

Step-by-step explanation:

The average salary in this city is $45,600.

Using the formula

z score = x - u /(sd/√n)

Where x is 46,356, u is 45,600 sd is 15,930 and n is 53.

z = 46,356 - 45600 / (15930/√53)

z = 756/(15930/7.2801)

z = 756/(2188.1568)

z = 0.3455

To draw a conclusion, we have to determine the p value, at 0.05 level of significance for a two tailed test, the p value is 0.7297. The p value is higher than the significance level, thus we will fail to reject the null and can conclude that there is not enough statistical evidence to prove that the average is any different for single people.

Answer:

84%

Step-by-step explanation:

We find the z-score here

z= x-mean/SD = 32-40/8 = -1

So the probability we want to find is;

P(z>-1)

This can be obtained using the standard score table

P(z>-1) = 0.84 = 84%

Answer:

[tex] \boxed{\sf Area \ of \ the \ rectangle = 91 \ yd^{2}} [/tex]

Given:

Length of the rectangle = 4 yd longer than its width

Perimeter of the rectangle = 36 yd

To Find:

Area of the rectangle

Step-by-step explanation:

Let the width of the rectangle be 'w' yd

So,

Length of the rectangle = (w + 4) yd

[tex] \therefore \\ \sf \implies Perimeter \: of \: the \: rectangle = 2(Length + Width) \\ \\ \sf \implies 36 = 2((4 + w) + w) \\ \\ \sf \implies 36 = 2(4 + w + w) \\ \\ \sf \implies 36 = 2(4 + 2w) \\ \\ \sf 36 =2(2w+4) \: is \: equivalent \: to \: 2(2w + 4) = 36: \\ \sf \implies 2(2w + 4) = 36 \\ \\ \sf Divide \: both \: sides \: of \: 2 (2w + 4) = 36 \: by \: 2: \\ \sf \implies 2w + 4 = 18 \\ \\ \sf Subtract \: 4 \: from \: both \: sides: \\ \sf \implies 2w = 14 \\ \\ \sf Divide \: both \: sides \: of \: 2w = 14 \: by \: 2: \\ \sf \implies w = 7[/tex]

So,

Width of the rectangle = 7 yd

Length of the rectangle = (7 + 4) yd

= 13 yd

[tex] \therefore \\ \sf Area \ of \ the \ rectangle = Length \times Width \\ \\ \sf = 7 \times 13 \\ \\ \sf = 91 \: {yd}^{2} [/tex]

Answer:

Step-by-step explanation:

(4x³ - 5x² + 3x ) - 4(5x² - 7x³ - 8x)

Remove the brackets and simplify.

We have

4x³ - 5x² + 3x - 20x² + 28x³ + 32x

Group like terms and simplify

That's

4x³ + 28x³ - 5x² - 20x² + 3x + 32x

We have the final answer as

- 3 - ( 4x + 3y - 2z ) - 4 + 2( 5x - 4y + 6z)

Remove the brackets and simplify

That's

- 3 - 4x - 3y + 2z - 4 + 10x - 8y + 12z

Group like terms and simplify

- 4x + 10x - 3y - 8y + 2z + 12z - 3 - 4

We have the final answer as

Hope this helps you

Answer:

D.

m = 2 = figures/month

b = 20 = # of action figures

Answer:

a. p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex]  

b.0.6 ±  1.96 [tex]\sqrt \frac{0.6* 0.4}{1000}[/tex]  

c. { -1.96 ≤  p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex]     ≥ 1.96} = 0.95  

Step-by-step explanation:

Here the total number of trials is n= 1000

The number of successes is p` = 600/1000 = 0.6. The q` is 1 - p`= 1- 0.6 = 0.4

The degree of confidence is 95 %  therefore z₀.₀₂₅ = 1.96 ( α/2 = 0.025)

a.  The formula used will be

p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex]       ( z with the base alpha by 2 (α/2 = 0.025))

b. Putting the values

0.6 ±  1.96 [tex]\sqrt \frac{0.6* 0.4}{1000}[/tex]  

c. Confidence Interval in Interval Notation.

{ -1.96 ≤  p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex]     ≥ 1.96} = 0.95  

{ -z( base alpha by 2) ≤  p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex]     ≥ z( base alpha by 2)  } = 1- α

Answer: 0.388 m

Step-by-step explanation:

Ok, if the ball is dropped from 1.8 meters, then the height after the first bounce will be 3/5 times 1.8 meters:

h1 = (3/5)*1.8m = 1.08m

now we can think that the ball is dropped from a height of 1.08 meters, then the height after the second rebound will be:

h2 = (3/5)*1.08m = 0.648m

Now, using the same method as before, the height after the third bounce will be:

h3 = (3/5)*0.648m = 0.388 m

Notice that we can write this relation as:

h(n) = 1.8m*(3/5)^n

where n is the number of bounces.

if n = 0 we have the initial height, and if n = 3 we are on the third bounce, then:

h(3) = 1.8m*(3/5)^3 = 0.388 m

Answer:

-3a

Step-by-step explanation:

3(-a)

Expand brackets.

3 × -1a

-3a

Answer:

-12,-10,-3,-1.4,-1,0.25,2,5.2,12

Step-by-step explanation:

The following number −1.4; 2; −3 1 2 ; −1; − 1 2 ; 0.25; −10; 5.2 in increasing order

-12,-10,-3,-1.4,-1,0.25,2,5.2,12

It's arranged this way starting from the negative sign because positive it's greater than negative and if the negative gets to approach zero it's get smaller

Answer:

-10 ; -3 1/2 ; -1.4 ; -1 ; -1/2 ; 0.25 ; 2 ; 5.2

Answer:

Probability that it'll not rain during the next three days = 0.064

Step-by-step explanation:

Given

Let:

P(R) represent the probability that it'll rain each day

P(R') represent the probability that it'll not

[tex]P(R) = 60\%[/tex]

Required

Probability that it'll not rain during the next three days

From concept of probability;

[tex]P(R) + P(R') = 1[/tex]

Substitute 60% for P(R)

[tex]60\% + P(R') = 1[/tex]

Subtract 60% from both sides

[tex]60\% - 60\% + P(R') = 1 - 60\%[/tex]

[tex]P(R') = 1 - 60\%[/tex]

Convert % to decimal

[tex]P(R') = 1 - 0.6[/tex]

[tex]P(R') = 0.4[/tex]

The probability that it'll not rain during the next 3 days is:

[tex]P(R') * P(R') * P(R')[/tex]

[tex]P(R') * P(R') * P(R') =0.4 * 0.4 * 0.4[/tex]

[tex]P(R') * P(R') * P(R') = 0.064[/tex]