An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 6.5 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 26 engines and the mean pressure was 6.6 pounds/square inch with a standard deviation of 1.0. A level of significance of 0.01 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Given:

The figure of a right angle triangle with hypotenuse 10 and two angles [tex]45^\circ, 90^\circ[/tex]

To find:

The lengths of the legs.

Solution:

Two angles are given. By using the angle sum property, the third angle is:

Third angle = [tex]180^\circ-45^\circ- 90^\circ[/tex]

                   = [tex]45^\circ[/tex]

Base angles are equal it means the given triangle is an isosceles right triangle. So, the lengths of both legs are equal.

Let x be the lengths of both legs. Then by using Pythagoras theorem, we get

[tex]Hypotenuse^2=leg_1^2+leg_2^2[/tex]

[tex](10)^2=x^2+x^2[/tex]

[tex]100=2x^2[/tex]

[tex]\dfrac{100}{2}=x^2[/tex]

[tex]50=x^2[/tex]

Taking square root on both sides, we get

[tex]\pm \sqrt{50}=x[/tex]

[tex]\pm 5\sqrt{2}=x[/tex]

[tex]\pm 5\sqrt{2}=x[/tex]

The side length cannot be negative. So, the only value of x is [tex]5\sqrt{2}[/tex].

Therefore, the length of the both legs is [tex]5\sqrt{2}[/tex] units.

Answer:

Alternative Hypothesis:H₁: μ ≠ 0.41

Step-by-step explanation:

Step(i):-

Given that the newscast reaches 41% of the viewing audience in the area

The mean of the Population = 0.41

Given that In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station

Given that the mean of the sample = 0.36

Step(ii):-

Null hypothesis: The sample statistic does not differ significantly from the hypothetical parameter value.

Given data

Null hypothesis: H₀ : μ = 0.41

Alternative Hypothesis: Any hypothesis which is complementary to the Null hypothesis

Alternative Hypothesis:H₁: μ ≠ 0.41

Answer:

I'm pretty sure it's 10,000

Answer:

61.73 ft ^2

Step-by-step explanation:

area of rectangle

14x8 = 112

area of circle

π(4)(4) = 50.27

subtract

112-50.27 = 61.73

Answer:

over 1/2 own a dog

Step-by-step explanation:

Answer:

Over 1/2 of students own a dog.

Step-by-step explanation:

Total number of students: 25 Add the students owning different types of pets

13/25 Number of students owning dogs divided by total number of students

13/26 = 1/2; therefore 13/25 > 1/2

Answer:x is a letter in music.} 3. Determine whether each set is well-defined. If it is not well-defined, explain why, ... true (e) {1, 3, 5, 7, 9) = {1, 5, 9, 3, 7) false_(f) {1,3,5, 9) = {1,3,5,9} ... Describe each of the following sets as either finite or infinite. ... 13 listened to heavy metal and alternative rock; 12 listened to rap and alternative rock;. or

x 2 - 2yZ = 7 with x = 2v + 1 and y = 2b + 1. These have solutions. (x, y; v, b) = (3, 1; 1,0), (5,3; 2,1), (13,9; 6,4),. (27,19; 13,9), (75,53; 37, 26), (157,111; 78, 55), .

Step-by-step explanation:

Answer:

A. Inscribed angle theorem

Step-by-step explanation:

The missing reasons in the proof are inscribed angles theorem​.

In mathematics, an arc is defined as a portion of the boundary of a circle or a curve. It can also be referred to as an open curve. The boundary of a circle is the perimeter or the distance around a circle, also known as the circumference.

Given that, a circle, with arcs AD and BC, we need to find the reason in the proof,

The reasons are inscribed angles theorem.

Inscribed angles theorem :-

The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle. Therefore, the angle does not change as its vertex is moved to different positions on the circle.

Hence the missing reasons in the proof are inscribed angles theorem​.

Learn more about arcs, click;

https://brainly.com/question/29886215

#SPJ7

Answer:

[tex]Range: 0 \le y \le 400[/tex]

Step-by-step explanation:

Given

[tex]Gas = 25 gallons[/tex]

[tex]Distance = 400miles[/tex] --- max

Required

The range of the function

The graph is not given; however, the question can be answered without the graph.

From the question, we understand that the truck can hold up to 25 gallons.

This represents the domain (i.e. from 0 to 25)

When the truck is empty (i.e. no gas in it), the truck cannot move any distance (0 miles).

When the truck is filled up (i.e. 25 gallon), the truck can move up to 400 miles.

This represents the range (i.e. from 0 to 400 miles)

Hence, the range is:

[tex]Range: 0 \le y \le 400[/tex]

Answer:

28,436,297,825

30,943,267,101

45,000,000,000

Step-by-step explanation:

ur welcome

Answer: 2880 hours

Explanation: 120 days times 24 hours

Answer:

20 oz.

Step-by-step explanation:

Hope this helps ! :)

Answer:

What do you mean? If you are talking about the Community not always answering Questions well that means your they don't know the right Answer

the Mods are Annoying and very skeptic of the Guidelines of Brainly.

Answer:

Pretty sure it would be b because it keeps scaling as the x axis continues with time

Answer:

You will pay 70% of the original price. You will pay $17.50

Step-by-step explanation:

100% is full price because 100%=1 (one whole).

100% - 30% = 70%

70% = 0.7

0.7 multiplied by $25 is $17.50

Answer:

24 2/5ft

Step-by-step explanation:

add all the sides together.

4ft x 2

3ft x 2      

10 2/5 x 1

=

24 2/5

Answer:56

Step-by-step explanation:

Answer: hope this helps

Step-by-step explanation:

Answer:

Hope this helped!!!

Step-by-step explanation:

Answer: 42 is not a square of a whole number

Step-by-step explanation: 81= 9², 100= 10², x²= x·x, 6²= 36 and 7²= 49

Answer

$266.66

Step-by-step explanation:

We have here ,

We can use the formula of SI to calculate the SI . After adding it to principal we will get the amount .

⇒ SI = P × R × T / 100

⇒ SI = $ 200 × 16 × 10 / 12 × 100

⇒ SI = $ 26.66

Now Calculate amount as ,

⇒ A = SI + P

⇒ A = $ 200 + $ 26.66

⇒ A = $ 226.66

Answer:

the angles are 120.1 and 59.9

Step-by-step explanation:

supplementary means that the add up to be 180

I made a system of equations and to make thing faster I graphed them but if you wanted you could solve fully

x+y=180

y-60.2=x

Answer:

A. Normal

B. Between 2.078 and 2.722 visits.

C. About 90 percent of these confidence intervals will contain the true population mean number of visits per week and about 10 percent will not contain the true population mean number of visits per week.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

Question A:

By the Central Limit Theorem, normal.

Question B:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.645\frac{2.9}{\sqrt{219}} = 0.322[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 2.4 - 0.322 = 2.078 visits

The upper end of the interval is the sample mean added to M. So it is 2.4 + 0.322 = 2.722 visits.

Between 2.078 and 2.722 visits.

Question c:

90% confidence level, so 90% will contain the true population mean, 100 - 90 = 10% wont.

About 90 percent of these confidence intervals will contain the true population mean number of visits per week and about 10 percent will not contain the true population mean number of visits per week.

Answer:median

Step-by-step explanation: because median is used to be in the middle so those are numbers that would be in the middle, and if you add them up it would contain a high amount of number but if you subtract half you get your answer, and your Welcom!

Answer:

d.

Step-by-step explanation:

line AG is the answer because a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior.

Answer:

d. line AG

Step-by-step explanation:

A tangent is a line that just 'touches' the curve of a circle, and doesn't intersect it.

We can see that since AG touches the circle, and since the other lines all intersect the circle, the tangent here is AG

Step-by-step explanation:

6/5is the answer................

Answer:

1 and 1/5

Step-by-step explanation:

6 times 1/5 is 1/5+1/5+1/5+1/5+1/5+1/5 which equals to 6/5 which also equals to 1 and 1/5

Answer:

140 cm^2

Step-by-step explanation:

Formula for area of a Parallelogram: base*height

14 cm * 10cm = [tex]140 cm^{2}[/tex]

9514 1404 393

Answer:

  0

Step-by-step explanation:

f(x) = x^3 is an odd function, so is symmetrical about the origin. Its average value on any symmetrical interval around the origin will be 0.

The average value is 0.

Answer:

Radius = 26 yards.

Step-by-step explanation:

The complete rotation of the sprinkler makes a circle of radius R (R is the length of the stream of water).

Remember that the area of a circle of radius R is:

A = pi*R^2

where pi = 3.14

In this case, we know that the area is equal to 2,200 yd^2

Then:

A = 2,200 yd^2 = 3.14*R^2

Solving this equation we can find the value R.

(2,200 yd^2)/3.14 = R^2

√( (2,200 yd^2)/3.14) = R  = 26.47 yards.

We want to round it to the nearest yard, then we need to look at the first digit after the decimal point. It is smaller than 5, then we round down, we get:

Radius = 26 yards.

Answer:

3/7

Step-by-step explanation: