Please answer..........................................

The z-score of 0.3162 is less than 2.33, we fail to reject the null hypothesis. There is not enough evidence to conclude that the valve performs above the specifications.

The null hypothesis is that the valve produces a mean pressure of 5.5 pounds/square inch. The alternative hypothesis is that the valve produces a mean pressure greater than 5.5 pounds/square inch.
The decision rule for rejecting the null hypothesis at a significance level of 0.01 is to reject it if the test statistic (z-score) is greater than 2.33.
To calculate the z-score, we use the formula:
z = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))
z = (5.6 - 5.5) / (0.8 / sqrt(18))
z = 0.3162
Since the z-score of 0.3162 is less than 2.33, we fail to reject the null hypothesis. There is not enough evidence to conclude that the valve performs above the specifications.

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The average force exerted by the press over the interval [0, pi/3] is 750N.

Force is a physical factor that alters or has the potential to alter an object's state of rest or motion as well as its shape. Newton is the SI unit of force.

Given

F(x) ∝ sec (x)

x = [0,Pi/3] range or x = [0 , 60°]

F is 500 N for x = 0,

so F(0) = 500 N.

As we are aware:

Since force is proportional to sec(x), the following equation may be written by introducing the proportionality constant (k):

Equation 1: F(x) = k * sec(x).

Consequently, considering the given data of F=500 N at x = 0, we have:

500 = k * sec(0)

Since sec(0) = 1, we obtain:

k = 500

Adding the value of k to equation 1 gives us:

F(x) = 500 * sec (x)

Now, by substituting Pi/3 for the maximum value of x from the provided range in the equation above, we obtain:

500 times pi/3 equals one second.

Pi equals 180, thus we may reduce the equation above as follows:

F(60°) = 500 * sec(60°)

F(60°) = 500 * 2, and

sec(60°) = 2 are obtained.

F(60°) = 1000 N

Now, the hydraulic press's average force is given by:

Minimum Force + [(Maximum Force - Minimum Force) / 2] = Average Force - Recitize equation 2.

Given that sec(x) has a minimum value at x = 0 and a maximum value at x = 60° within the range [0, 60°], we can write as follows:

F = 500 N is the minimum force applied at x = 0 and F = 1000 N is the maximum force applied at x = 60°.

Finally, using equation, we obtain the average force.2 as follows:

Average force is equal to 500 plus [(1000 - 500)/ 2].

Force Average = 500 + 250

750 N is the average force.

The average force exerted by the press over the interval [0, pi/3] is 750N.

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The probability is h(x; 7, 4, 9) = [x(4 - x)] / 126 and the number of top four candidates that can be expected to be interviewed on the first day is 3.11.

(a) The probability that x of the top four candidates are interviewed on the first day is given by the hypergeometric probability distribution function, which is h(x; 7, 4, 9). The values of n, m, and k are 9, 4, and 7, respectively. Therefore, the probability is:

h(x; 7, 4, 9) = [mCx * (n - m)C(k - x)] / nCk= [4C x  * 5C(7-x)] / 9C7= [4!/(x!(4-x)!) * 5!/(7-x)!] / 9!/(7!2!) [n!/(n - k)!k!]

On simplification, we get: h(x; 7, 4, 9) = [x(4 - x)] / 126

The probability that x of the top four candidates are interviewed on the first day is h(x; 7, 4, 9) = [x(4 - x)] / 126

(b) The expected number of the top four candidates to be interviewed on the first day is given by the mean of the hypergeometric probability distribution function, which is np. Therefore, the expected number of candidates is: np = 7(4/9) = 3.11 (rounded to two decimal places)

Hence, the number of top four candidates that can be expected to be interviewed on the first day is 3.11.

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The original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

To show that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves, we need to take the derivative of the equation and set it equal to -1/b^2, the slope of the orthogonal line.

First, we take the derivative of the equation with respect to x:

2x/a^2 = -2y/b^2 * dy/dx

Simplifying, we get:

dy/dx = -b^2*x/a^2*y

Now, we set this equal to -1/b^2:

-b^2*x/a^2*y = -1/b^2

Cross-multiplying and simplifying, we get:

x/a^2*y = 1/b^2

Finally, we can rearrange this equation to get:

y = b^2*x/a^2

This equation represents the orthogonal family of curves to the original family of conics. Since the original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

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\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\(\qquad \tt \rightarrow \: slope \:\: of \:\: line = \cfrac{3}{2}\)

____________________________________

\( \large \tt Solution \: : \)

The equation of line is written in slope - intercept form

\(\qquad \tt \rightarrow \: f(x) = \dfrac{3}{2} x - 4\)

if we compare it with general slope - intercept equation of line :

\(\qquad \tt \rightarrow \: f(x) = mx + c\)

[ m represents slope of line ]

\(\qquad \tt \rightarrow \: m = \dfrac{3}{2} \)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

\(\frac32\)

Step-by-step explanation:

Hello!

An equation of a line is usually written in slope-intercept form.

Slope Intercept Form: \(y = mx + b\)

If we compare our given equation with the format:

This means that \(\frac32\) would be our slope for the line.

The area of a circle is given by:

Where π ≅ 3.14 and d is the diameter of the circle.

Now, a semi-circle is a half of a circle, so its area is half of the area of the complete circle:

Replacing the value d = 14 in the last formula, we get:

Answer

The area of a semicircle with a diameter d =14 is approximately 76.97 units square.

Atticus asks Calpurnia to go with him to tell Helen Robinson about the death of her husband. Option B is the correct answer.

Helen Robinson was Tom Robinson's widow in To Ki-ll a Mockingbird, a novel by Harper Lee. Despite the fact that she is not a major character in the story, she plays a significant role in the novel's plot. When Bob Ewell accuses Tom Robinson of ra-pe, Atticus Finch is hired to defend him, and Helen Robinson appears in the story.

When Tom Robinson, a black man, was accused of rapi-ng a white woman, Mayella Ewell, he was arrested and imprisoned in the local jail. He was sentenced to death, but he attempted to flee and was subsequently sh-ot and kill-ed by a group of guards. When the news of his death reaches Atticus, he goes to tell Helen Robinson that her husband had died.  Atticus, recognizing that it will be difficult for her to receive such news, offers to accompany her and asks Calpurnia to come along with him.

Calpurnia was the Finch family's black housekeeper in the novel To K-ill a Mockingbird. She is one of the few African American characters in the book who has a speaking role, and she serves as a motherly figure to Scout and Jem. Throughout the novel, she serves as a bridge between the white and black communities, and she plays a crucial role in the story's resolution.

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Answer:

644cm^3

Step-by-step explanation:

r = 2.25 cm

h = 4.5*3= 13.5

volume =

\((4 \div 3) \times \pi \times {r}^{3} \)

= 644 cm^3

The correct sampling method described in the question is a stratified random sample among the simple random sample,  stratified random sample, cluster random sample and  Voluntary random sample

The sampling method described in the question is a stratified random sample.

In a stratified random sample, the population is divided into subgroups or strata based on certain characteristics or criteria. Then, a random sample is selected from each stratum. The key idea behind this method is to ensure that each subgroup is represented in the sample proportionally to its size or importance in the population. This helps to provide a more accurate representation of the entire population.

In the given sampling method, the population is divided into subgroups, and a fixed number of units is taken from each group. This aligns with the process of a stratified random sample. The sample selection is random within each subgroup, but the number of units taken from each group is fixed.

Other sampling methods mentioned in the question are:

Simple random sample: In a simple random sample, each unit in the population has an equal chance of being selected. This method does not involve dividing the population into subgroups.

Cluster random sample: In a cluster random sample, the population is divided into clusters or groups, and a random selection of clusters is included in the sample. Within the selected clusters, all units are included in the sample.

Voluntary random sample: In a voluntary random sample, individuals self-select to participate in the sample. This method can introduce bias as those who choose to participate may have different characteristics than those who do not.

Therefore, the correct sampling method described in the question is a stratified random sample.

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The dimensions of the can that minimize the cost of the material are approximately:

Radius (r) ≈ 6.324 cm

Height (h) ≈ 3.984 cm

To determine the dimensions of the can that minimize the cost of the material, we need to find the dimensions that minimize the surface area of the can.

Let's assume the can has a height of h and a radius of r.

The volume of a cylinder is given by:

V = πr²h

Given that the can should hold 500 cubic centimeters of liquid, we have:

500 = πr²h

We want to minimize the cost, which depends on the surface area of the can.

The surface area of the can is the sum of the areas of the top, bottom, and side surfaces.

The cost of the top and bottom surfaces is twice as expensive per square centimeter as the sides.

Let's assume the cost per square centimeter of the sides is c, so the cost per square centimeter of the top and bottom surfaces is 2c.

The surface area of the sides of the cylinder is given by:

A_sides = 2πrh

The surface area of the top and bottom surfaces (each) is given by:

A_top_bottom = 2πr²

The total surface area (cost) is given by:

Cost = 2(2c)A_top_bottom + cA_sides

= 4cπr² + 2c(2πrh)

= 4cπr² + 4cπrh

To minimize the cost, we need to minimize the surface area. To do this, we can express the surface area in terms of a single variable, such as the radius (r) or the height (h).

From the volume equation, we have:

h = 500 / (πr²)

Substituting this value of h into the surface area equation, we get:

Cost = 4cπr² + 4cπr(500 / (πr²))

= 4cπr² + 2000c/r

Now, we can take the derivative of the cost function with respect to r, set it equal to zero, and solve for r to find the critical points:

dCost/dr = 8cπr - 2000c/r² = 0

8cπr = 2000c/r²

8πr³ = 2000

r³ = 250 / π

r ≈ 6.324

Now, we can substitute this value of r back into the equation for h:

h = 500 / (π(6.324)²)

≈ 3.984

So, the dimensions of the can that minimize the cost of the material are approximately:

Radius (r) ≈ 6.324 cm

Height (h) ≈ 3.984 cm

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Answer:

X=14

Side GF: 41 ft

Side FE: 58 ft

Side DE: 98 ft

Side DG: 28 ft

Step-by-step explanation:

(13+2x)+(4x+2)+(7x)+(X+14)

6x+15+8x+14

14x+29=225

     -29.  -29

     14x=196

      /14.  /14

        X=14

Fill in 14 for x for each side

13+2(14)

13+28

Side GF: 41 ft

4(14)+2

56+2

Side FE: 58 ft

7(14)

Side DE:98 ft

14+14

Side DG: 28 ft

Hopes this helps please mark brainliest

The function for acceleration is a(t) = 6t³ + 54t² + 144t.

To find where the velocity is equal to zero, we need to solve the equation v(t) = 0. Given that the velocity function v(t) is not provided in the question, we'll have to integrate the given acceleration function to obtain the velocity function.

To find the velocity function v(t), we integrate the acceleration function a(t):

v(t) = ∫(6t³ + 54t² + 144t) dt

Integrating term by term:

v(t) = 2t⁴ + 18t³ + 72t² + C

Now, to find the specific values of t for which the velocity is equal to zero, we can set v(t) = 0 and solve for t:

0 = 2t⁴ + 18t³ + 72t² + C

Since C is an arbitrary constant, it does not affect the roots of the equation. Hence, we can ignore it for this purpose.

Now, let's find the function for acceleration a(t). It is given as a(t) = 6t³ + 54t² + 144t.

Therefore, the function for acceleration is a(t) = 6t³ + 54t² + 144t.

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On solving the provided question, we can say that The urn contains 1 WIN and 4 LOSE balls - P(W) = 1 / 1+4 = 1/5 ; P(L) = 4/5 and  Probability (WIN) = 5/9

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

ball is drawn on the i th drawn

The draws are mutually independent , because the sampling OCCUrs with replacement

The urn contains 1 WIN and 4 LOSE balls.

P(W) = 1 / 1+4 = 1/5

P(L) = 4/5

If the white balls are pulled on an odd draw, you win if you draw first (since you draw on the odd draws and your opponent draws on the event draws). You should be aware that if you win on an unusual draw—one that is not the initial draw—all preceding draws must have resulted in LOSE balls.

Probability (WIN) = 5/9

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The measure of angle EBF is  80° .

In the question ,

it is given that ,

point A, B and C lie on a straight line .

and G , B and F lie on a different straight line .

angle GBA = 24° so ,

GBA + GBC = 180°   ...because linear pair

So , GBC = 180 - 24 = 156°

angle CBF = 24°          ......because vertically opposite angles are equal .

from the figure , we see that angle GBC and angle ABF are vertically opposite angles , so ,

156° = ABE + EBF         .....(1)

Since the line AC and DF are parallel and BE is the transversal

So  , angle DEB + angle ABE = 180°

104° + ABE = 180°

ABE = 180-104

ABE = 76°

Substituting ABE = 76° in the equation (1) ,

we get ,

156 = 76+ EBF

EBF = 156 - 76

EBF = 80°

Therefore , The measure of angle EBF is  80° .

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Answer:

\(k\le \:-18\)

Step-by-step explanation:

First, you add 66 to both sides so then the equation you are trying to solve will be: \(k-66+66\le \:-84+66\)

Finally, you simplify and get: \(k\le \:-18\)

Hope this helped!

b. A variable annuity.

P did not buy a variable annuity. Variable annuities are investment products that allow individuals to allocate their annuity funds among various investment options. The income stream from a variable annuity is not fixed and can fluctuate based on the performance of the chosen investments.

In this case, P is looking for a lifetime income stream beginning at age sixty, which indicates a desire for a fixed income. Therefore, P most likely purchased a straight life annuity, an immediate annuity, or a deferred annuity, all of which provide a fixed income stream.

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Answer:

3^3 = 27

27 * 3.14 = 84.78

84.78 * 4/3 = 113.04 is your answer.

Formula of volume of sphere is:

4/3 x π(3.14 or 22/7 whatever they tell you to use for pi) x r^3(your radius being cubed)

You get your radius by finding out what is half of your diameter or your given radius.

Answer:

124

Step-by-step explanation:

5 out of 40 = ⅛ of the students stated they would like to have a school uniform policy.

992 × ⅛ = 124

Answer:

218,048. skeins

Step-by-step explanation:

This question is built to throw you off by not telling you about the information in order.

First, the polypay sheep produces 9.9 pounds of wool.

Then, each pound produces 10.95 miles of yarn.

And finally, the yarn is packaged into skeins that are 175 yards each.

Each polypay sheep is 9.9 pounds. And we will use that total weight to find the amount of yarn in miles.
Then we will split up that yarn into equal pieces to make skeins.

BUT, the pieces are measured in yards, so we will have to convert the miles of yarn into an equivalent amount in yards as well. (Unmatched units of measurements don't mix well).

So, our equation will look like this:

(#of sheep) \(\times\) (9.9 pounds per sheep) \(\times\) (10.95 miles per yarn) \(\times\) (1760 yards per mile) \(\div\) (175 skeins per yard)

The number of sheep Bill has is 200.

So, we plug that into the number model we made.

\(200\times9.9\times10.95\times1760\div175\)

We end up with:

218,048.914

The decimal indicates that there is a remaining amount of yarn that couldn't be properly packaged into a skein.

Since, that remainder is not a complete skein, we must ignore its existence.

So the number of skeins expected is:

218,048

The number of skeins of yarn is Bill's flock expected to produce in one year is 1819.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, a polypay sheep produces an average 9.9 pounds of wool annually.

Farmer Bill has a flock of 200 polypay sheeps

So, total weight of wool is 9.9×200

= 1980 pounds

One pound of wool makes 10.95 miles of yarn.

So, the number of yarns = 1980/10.95

= 180.82 miles of yarn

We know that, 1 mile =1760 yards

Then, 180.82 miles

= 318243.2 yards

This wool is cleaned, spun into yarn and then packaged into skeins of 175 yards of yarn each.

Number of skeins = 318243.2/175

= 1819

Therefore, the number of skeins of yarn Bill's flock expected to produce in one year is 1819.

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Answer:

31 is the answer of this question

Answer:

31 and my day was good how was yours?

Step-by-step explanation:

Answer:

7 \(\frac{5}{8}\)

Step-by-step explanation:

4 \(\frac{1}{4}\) + 3\(\frac{3}{8}\)  we need a common denominator and that would be 8

4 \(\frac{1}{4}\) = 4\(\frac{2}{8}\)  (\(\frac{1}{4}\) x \(\frac{2}{2}\) makes the equivalent fraction \(\frac{2}{8}\))

4\(\frac{2}{8}\) + 3\(\frac{3}{8}\) = 7\(\frac{5}{8}\)

Answer:24200

Step-by-step explanation:

I=PxRxT

20000x.07x3=4200

20000+4200=24200

Answer:

2n+2

Step-by-step explanation:

I hope this helps and can I have brainliest!

Answer:

The 3rd one, 10.5+(-7.5)+12

Step-by-step explanation:

If something is +(-), the answer is minus.

So therefore 10.5-7.5+12 would be our answer

Which is equivalent to the original expression

Hope this helps!

Answer:

4 ( 2x + 3 )     do order of operation 4 times 2x plus 4 times 3

8x + 12

Step-by-step explanation:

hope it helped

Answer: 8x + 12

Step-by-step explanation:

4(2x+3)

Use distribution

8x+12

Answer:

lesser x =-4

greater x =1/2