A major car manufacturer wants to test a new engine to determine if it meets new air pollution standards. The mean emission, μ, of all engines of this type must be approximately 20 parts per million of carbon. If it is higher than that, they will have to redesign parts of the engine. Ten engines are manufactured for testing purposes and the emission level of each is determined. Based on data collected over the years from a variety of engines, it seems reasonable to assume that emission levels are roughly Normally distributed with σ = 3 parts per million of carbon. What are the appropriate null and alternative hypotheses?

Answer:

(a) and (c)

Step-by-step explanation:

Given

See attachment for complete question

Required

Select all true statements

First, calculate the total observed frequency;

[tex]Total = 11 + 16 + 14 + 20 + 12 + 17[/tex]

[tex]Total = 90[/tex]

(a): Relative frequency of 4 is 2/9

Relative frequency is calculated by:

[tex]RF= \frac{Observed\ Frequency}{Total}[/tex]

For roll 4

[tex]Observed\ frequency = 20[/tex]

So, the relative frequency is:

[tex]RF = \frac{20}{90}[/tex]

Simplify

[tex]RF = \frac{2}{9}[/tex]

(a) is true

(b): Experimental probability of 3 greater than its theoretical probability

The experimental probability is its relative frequency;

For roll 3

[tex]Observed\ frequency = 14[/tex]

The experimental probability is:

[tex]Pr = \frac{14}{90}[/tex]

Simplify

[tex]Pr = \frac{7}{45} = 0.156[/tex]

To calculate  the theoretical probability, w have:

[tex]S = \{1,2,3,4,5,6\}[/tex] ---- sample space

[tex]n(S)= 6[/tex]

[tex]n(3) = 1[/tex] --- number of times 3 occur

The theoretical probability is:

[tex]Pr = \frac{1}{6} = 0.167[/tex]

The theoretical probability is [tex]greater\ than\ the[/tex] experimental probability.

(b) is false

(c): Experimental probability of 2 greater than its theoretical probability

Using the explanations in (b), we have:

For roll 2

[tex]Observed\ frequency = 16[/tex]

The experimental probability is:

[tex]Pr = \frac{16}{90}[/tex]

Simplify

[tex]Pr = \frac{8}{45} = 0.178[/tex]

To calculate the theoretical probability, we have:

[tex]n(S)= 6[/tex]

[tex]n(2) = 1[/tex]

The theoretical probability is:

[tex]Pr = \frac{1}{6} = 0.167[/tex]

The experimental probability is [tex]greater\ than\ the[/tex] theoretical probability.

(c) is true

(d): Relative frequency of 5 is 2/13

For roll 5

[tex]Observed\ frequency = 12[/tex]

The relative frequency is:

[tex]RF = \frac{12}{90}[/tex]

Simplify

[tex]RF = \frac{2}{15}[/tex]

(d) is true

Answer:

Person above/under me is incorrect

Step-by-step explanation:

Answer is A and D Because i got their answer wrong

Answer:

a) (3,7) b) 35

Step-by-step explanation:

Answer:

second

Step-by-step explanation:

according to law of indicies

order goes upon the power

n root a

= a power 1/n

Answer:

:D

Step-by-step explanation:

if the parent function, y=f(x) has a number added (y=f(x)+4) the graph will be translated up. If the parent function has a number subtracted, y=f(x)-4, the graph will be translated down. The image explains more simply, and there are more possible translations (shown in image)

Answer:

The answer is (13,48,50)

Answer:

(2x^2+6x+3)(2x+4)

Step-by-step explanation:

Step-by-step explanation:

here's your solution

==> by using Pythagoras theorem

==> base^2 = hypotenuse^2 - perpendicular^2

==> hypotenuse = 18 , perpendicular = 16

==> base^2 = 18^2 - 16^2

==> base^2 = 324 - 256

==> base^2 = 68

==> base = √68

==> base = 8.24

[tex]hope \: it \: helps[/tex]

Answer:5 I think

Step-by-step explanation:

75-35=40 40 divided by 8 is 5

Answer:

The answer is 5=x (he is able to buy 5 videogames)

Step-by-step explanation:

First, you need to put this into an equation format with a variable (x) for the videogames. Here is what the equation should look like: 75 = 35 + 8x

75 being the total amount of money he has to spend, 35 being what he had to spend or knows he will spend on the controller, and the 8 is for each videogame. We put an 'x' behind the 8 to signal that we don't know how many games he can buy. So, then we need to solve the equation.

75=35+8x

-35 on both sides

So, 40=8x, then you divide by 8 to get x by itself

5=x

The 'x' in this equation is how many videogames he is able to buy. The way you could check your work is if you plugged 5 back into x. What I mean is this: 35+8(5) needs to equal 75, and it does, so you're good!

Answer:

OC. log,8

Step-by-step explanation:

5 log,2 -log,4, = 0.903089987

log,8, = same as above

The expression  [tex]5log2-log4[/tex] is equivalent to  [tex]log8[/tex]  which is option c.

A logarithm answers the question "How many of this number do we multiply to get that number?" Example How many 2s must we multiply to get 8 that is 3.

Given,

[tex]5log2-log4[/tex]

= [tex]log2^5-log4[/tex]

= [tex]log32-log4[/tex]

= [tex]log\frac{32}{4}[/tex]

= [tex]log8[/tex]

Hence, the expression  [tex]5log2-log4[/tex] is equivalent to  [tex]log8[/tex] .

Learn more about Log:

https://brainly.com/question/10028985

#SPJ2

Answer:

the correct answer is 27%

Answer:

27%

Step-by-step explanation:

to find percent use

8 x

----- × -----

30 100

then cross multiply 8 & 100 to get 800

divide 800 by 30 to get 26.6 repeating

then im assuming you round.

Answer:

c

Step-by-step explanation:

np!

Answer:

B

Step-by-step explanation:

since it is A over H (SohCahToa)

The equation of the red graph is,

⇒ y = x² + 4

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The equation of blue graph is,

⇒ y = x²

Since, We have;

The red graph is 4 unit up from the blue graph.

Hence, The equation of the red graph is,

⇒ y - 4 = x²

⇒ y = x² + 4

Therefore, The equation of the red graph is,

⇒ y = x² + 4

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ7

Answer:

C

because

[tex]42 \div 7 = 6 \\ 7 \times 6 = 42[/tex]

Part B: 65

Part A: Since there are 30 students of the class and 17 are boys, there are 13 girls. 13/30 = 43.33 = 43%.

Part B: Since 43% of the class are girls, we do 150*0.43 for the whole 7th grade which is 64.5 which I rounded to 65.

Answer:

One of them is 2 but I don't know the other one

Step-by-step explanation:

Answer:

Given, ∠MNP=107 degree.

Therefore, ∠QPN= 107 degree. [as, MN=PQ]

We know, sum of four angles of a quadrilateral is 360 degree.

And as MN=PQ, ∠NMQ=∠MQP.

Therefore, ∠MQP= {360 degree-( 107degree+ 107 degree)}/2

                             =( 360 degree-214 degree)/2

                            = 146 degree/2

                            =73 degree.

hope this will help you.

Step-by-step explanation:

Answer:

9.75

Step-by-step explanation:

10-0.25=9.75

The distance R from A and the bearing of R from A​ 15 km and 189° respectively.

The law of sine or the sine law states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

The law of cosine states that the square of any one side of a triangle is equal to the difference between the sum of squares of the other two sides and double the product of other sides and cosine angle included between them.

Given that, a village R is 10 km from a point P on a bearing 25° from P. Another village A is 6 km from P on a bearing 162°.

We need to calculate, the distance R from A and the bearing of R from A​

We will use the Cosine Rule to determine the distance of R from A (p);

From Cosine Rule;

b² = a² + c²– 2ac Cos B

p² = a² + r² – 2ar Cos P

a= 10 km

Cos P = Cos 137

r = 6 km

p = ?

p² = a² + r² – 2ar Cos P

p² = 10² + 6² - 2 (10) (6) Cos 1370

p² = 100 + 36 – 120 (- 0.7314)

p² = 136 + 87.76

p² = 223.76

p = 14.95 = 15 km (approximated to the nearest km)

To find the bearing of the R from A,

we will apply Sine Rule;

From Sine Rule;

15Sin Ø = 10Sin 137 = 6.82

Sin Ø = 6.82/15 = 0.4547

Ø = ArcSin 0.4547 = 27°

Therefore, the bearing of R from A will be

∠ PRA = 180 – 137 – 27 = 160

The alternating angle to 25° at R is 65°

Then, the bearing of R from A = 270 -65-16 = 189°

Hence, the distance R from A and the bearing of R from A​ 15 km and 189° respectively.

Learn more about sine, cosine rule, click;

https://brainly.com/question/26952873

#SPJ2

Answer:

313(?)

Step-by-step explanation:

qasxx c.f. tikhg

Answer:

4 and 9

Step-by-step explanation:

here's how it should be:

(36÷4) - (36÷9)

9 - 4

5

Answer:

(36 ÷ 4) − (36 ÷ 9) = 5

Step-by-step explanation:

To solve, we need to find the quotient of 36 divided by each number listed:

 ║12 ⇒ 36 ÷ 12 = 3

 ║8 ⇒ 36 ÷ 8 = 4.5

 ║9 ⇒ 36 ÷ 9 = 4

 ║4 ⇒ 36 ÷ 4 = 9

So, which of these two numbers can you subtract from each other to get 5?

 ║We can subtract 4 from 9 to get 5.

Therefore, our answer should be:

 ║(36 ÷ 4) − (36 ÷ 9) = 5

Answer:

4/7

Step-by-step explanation:

ajsgskajsgsujavagajana ahakangssua

The probability of the complement of event A P(Ac), which is the event of a place to not be a city, is 4/7. Option C is correct.

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

A place from this table is chosen at random. Let event A= the place is a city.

The total number of places are 7 given in the table.There are total three places which are city. Thus, the probability of a country to be a city is,

[tex]P(A)=\dfrac{3}{7}[/tex]

Now, for its complement, the probability of a place not be a city is,

[tex]P(A^c)=1-\dfrac{3}{7}\\P(A^c)=\dfrac{7-3}{7}\\P(A^c)=\dfrac{4}{7}[/tex]

Thus, the probability of the complement of event A P(Ac), which is the event of a place to not be a city, is 4/7. Option C is correct.

Learn more about the probability here;

https://brainly.com/question/24756209

#SPJ2

Answer:

17.20

Step-by-step explanation:

Let me know if this is right or not.

Answer:

Step-by-step explanation:

use pythagorean theorem which is c=square root of a2+b2

but we solving side be so

b=square root of c2-a2

b= square root (196-100)

b2=96

b approximately = 9.8

Answer:

C. Full of

Step-by-step explanation:

Ous is defined as full of or possessing. An example of ous used as a suffix is in the word "contemptuous," which means full of contempt. Moreover, how does the suffix ous change a word? Adding the suffix -ous A suffix is a letter or a group of letters that can be added to a word to change its meaning.

I hope this helps :3

-ous means "full of".

When someone is courageous, they have a lot of courage

When someone is gracious, they have a lot of grace

Answer: it is 3 definitely

Step-by-step explanation:

There are 4 people and each are getting one drink for 1.50 and 3 tacos so it makes sense to do 4 ( 1.50 + 3x ) by the way x stands for the money for the tacos

Answer:

The first step is to determine the largest number that evenly divides the numerator and the denominator (also called the Greatest Common Factor of these numbers). In other words, what's the biggest number that goes into '2' (the numerator) and '4', the denominator?

Step 2. Once you've answered step 1 and realized that, for our fraction at least, the greatest number that evenly divides 2 and 4 is '2'. Now divide the top and the bottom by 2 to get your simplified fraction which is ½.

I hope this helps if you have any questions on my answer plz let me know Ty :3

Answer:

find the greatest common factor, then divide the bottom and the top, and you have that as your answer

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

$1.26

Step-by-step explanation:

So you just have to find 2.25% of 56.

To find a certain percentage of something, you multiply it. Let's write out a sentence explaining what you need to do. You have to find:

2.25% of 56

Whenever you've got a sentence like this, all you've got to do is change the word "of" to a multiplication symbol. And now you've got an expression:

2.25% × 56

Let's convert the percentage to a decimal. To do this, you simply remove the percent symbol, then move the decimal point 2 places to the left.

2.25% = 0.0225

And now you have:

0.0225 × 56

Then you just do the math! I am assuming you already know how to do decimal multiplication so I'm not going to explain the process here.

But once you multiply 0.0225 × 56, you get an answer: 1.26

Hope this was helpful to you, and don't forget to choose the Brainliest answer!

Answer:

Step-by-step explanation:

volume of sphere = 4πr³/3

= 4π×512/3

≈ 2143.6 cm³

Answer:

(x+6)(x+4)

Step-by-step explanation: