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 8.0 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 24 engines and the mean pressure was 8.4 pounds/square inch with a standard deviation of 1.0 A level of significance of 0.05 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.

Answer:

10

Step-by-step explanation:

100 = 10 x 10 = 10^2

n^2  = 10^2

n = 10

The option that is not one of the application described is C. Building a bridge.

Origami created through mathematical interpretation and computation is known as mathematical origami, and it has resulted in the modeling of numerous novel origami-based structures outside of the realm of the arts. Furthermore, mathematical origami inspires the creation of new structures and mechanisms in engineering.

Origami-inspired engineering has been used in NASA space equipment, the development of better heart stents, and even DNA folding in microbiology.

Origami-based designs are the use of the ancient art of origami to solve various engineering problems. Regardless of the scale at which they are implemented, origami-based designs are always defined by the laws that govern their geometrical properties at any scale.

Furthermore, for large flat structures, origami allows for the reduction of dimensions while ensuring simple deployment this is especially useful for solar arrays in space applications.

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The Video "The Math and Magic of Origami" describes several examples in which scientists and engineers use origami to solve problems. Which of the following is NOT one of the applications described?  

A.A heart stent

B. A space telescope

C. Building a bridge

D. Air bags in cars

Triangle PQR after 270° counter-clockwise rotation has coordinates                      P'(-8,13)

Q'(-2,7)

R'(-7,6)

What is 270° counter-clockwise rotation?

When rotating a point 270 degrees counterclockwise about the origin our point A(x, y) becomes A'(y, -x). This means, we switch x and y and make x negative.

Solution:

Given: P (-13,3) , Q (-7, 3), R(-6, -2)

After 270° counter clockwise rotation about point C(-5 , -4)

P'(-3-5, 13), Q'(3-5, 7) , R'(-2-5, 6)

∴ P'(-8, 13), Q'(-2, 7), R'(-7, 6)

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Triangle PQR after 270° counter-clockwise rotation has coordinates             P'(-8,13)

Q'(-2,7)

R'(-7,6)

It is referred to as counter-clockwise rotation when something rotates in the opposite direction from how a clock's hands spin. Alternatively referred to as the anticlockwise direction, counter-clockwise rotation is the preferred term.

Counter clockwise examples include turning a screw, a lock, or a tap the opposite way from how it should be done in order to open them.

Solution:

Given: P (-13,3) , Q (-7, 3), R(-6, -2)

After 270° counter clockwise rotation about point C(-5 , -4)

P'(-3-5, 13), Q'(3-5, 7) , R'(-2-5, 6)

∴ P'(-8, 13), Q'(-2, 7), R'(-7, 6)

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Answer:v=2.5

Step-by-step explanation:

isolate the variable by dividing both sides by 5

v=2.5

The expected winnings are $3 for each time that you play the game.

What is expected winnings?

The expected value is a generalization of the weighted average in probability theory. Informally, the expected value is the arithmetic mean of a significant number of outcomes of a random variable that were independently chosen.

For an event with the outcomes {x₁, x₂, x₃,...} each one with correspondent probabilities {p₁, p₂, ...}

The expected value (here is equivalent to the expected winnings) is given by:

EV = x₁*p₁ + x₂* p₂ + ...

Here the outcomes are:

Winning $20, this happens if you draw a green marble, and there are:

7 green ones

3 yellow ones

10 black ones.

So 7 out of 20, then the probability is p₁ = 7/20

The second outcome is win $30 if you get a yellow one, there are 3 yellow ones, so the probability is p₂ = 3/10

Finally, you lose $15 if you get a black one, the probability now is

p₃ = 10/20

Then the expected winnings (remember that costs $1 to play, so we need to take that in consideration) is:

W = -$1 + $20*(7/20) + $30*(3/20) - $15*(10/20) = $3

Hence, the expected winnings are $3 for each time that you play the game.

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Answer:The relative change is a fraction that describes the size of the absolute change in comparison to the reference value: relative change = absolute change reference value = new value − reference value reference value . 100 100 = 100%. When a quantity triples in value, its relative change is 2 = 200%.

Step-by-step explanation:

The most common way to represent the absolute value of a number or expression is to surround it with the absolute value symbol: two vertical straight lines. |6| = 6 means “the absolute value of 6 is 6.” |–6| = 6 means “the absolute value of –6 is 6.” |–2 – x| means “the absolute value of the expression –2 minus x.”

Answer:

74.36

Step-by-step explanation:

the equlabruum is very important to me so I can do you have any questions or concerns please visit the plug-in settings for this is a very

Volume of a cube = 5 * 5 * 5; Volume of a cube = 125 The Lateral Surface Area of a Cube is Lateral Surface Area of a cube = 4 * length * length

The expected winnings are $3 for each time that you play the game.

For an event with the outcomes {x₁, x₂, x₃,...} each one with correspondent probabilities {p₁, p₂, ...}

The expected value (here is equivalent to the expected winnings) is given by:

EV = x₁*p₁ + x₂* p₂ + ...

Here the outcomes are:

Winning $20, this happens if you draw a green marble, and there are:

7 green ones

3 yellow ones

10 black ones.

So 7 out of 20, then the probability is p₁ = 7/20

The second outcome is win $30 if you get a yellow one, there are 3 yellow ones, so the probability is p₂ = 3/10

Finally, you lose $15 if you get a black one, the probability now is p₃ = 10/20

Then the expected winnings (remember that costs $1 to play, so we need to take that in consideration) is:

W = -$1 + $20*(7/20) + $30*(3/20) - $15*(10/20) = $3

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The value of the expression 2/125x1013 + 2/27x1013 is 91.248.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

The expression will be Illustrated as:

2/125x1013 + 2/27x1013

= (0.016 × 1013) + (0.0740741 × 1013)

= 16.208 + 75.04

= 91.248

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Complete question

2/125x1013 + 2/27x1013

Answer:

x=1

Step-by-step explanation:

The binary form can be represented as AB or AABB. So the write option is b.

One of the four different kinds of number systems is the binary number system. When used in computer programmes, binary numbers are solely represented by the digits 0 (zero) and 1. (one). Here, the base-2 numeric format is used to express the binary numbers.

Because the binary system is directly implemented in electronic circuits using logic gates, nearly all modern computers and computer-based gadgets employ it internally. A bit is used to describe each digit.

The binary form is a set of alphabetical character that is used to describe a musical piece using two sections of equal length. It can be represented as AB or AABB. So the write option is b.

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Answer:

[tex]f(x) > \sqrt{1 -x}[/tex]

which is the third choice

Step-by-step explanation:

We could just plot each and see which plot corresponds to the given graph

However, that is not necessary.

First note that the plot is a dotted line. This means the inequality is either a < inequality or a > inequality. If it were a ≤ or  ≥ inequality, the plot of the line would be a solid line

That eliminates first and last choices

To see which of the remaining two options fits the graph, take a point in the shaded region and see which one satisfies which inequality .

Checking second choice....

Point (0, 2) is in the shaded region
Does (0, 2) satisfy the second choice:  [tex]f(x) < \sqrt{1-x}\;\; ?[/tex]
Let's check by substituting 0 for the value of x
[tex]1-x = 0\; so \; \sqrt{1-x} = \sqrt{0} = 0[/tex]

But the corresponding value of y should be 2, not 0 so this inequality is not satisfied for a point in the shaded region. Eliminate second choice

Third choice is the correct answer

The required hourly wage of Mr. Freeze is given as $217.8.

Wage is defined as the defined earnings of the worker for their respective work. It can be evaluated in parameters based on degrees of time and difficulty.

Here,
As mentioned in the question,
Mr. Freeze is paid $30 per pound of ice,
it took him 73 hours to sculpt 5 sculptures weighing a total of 530 pounds.
Total ice he used = 530 pounds,
For 530 pounds of ice Mr. Freeze gets paid,
= 530 × 30
= $15900

Now, Divide the whole amount for a pound of ice by the total hours Mr. Freeze works so we get the hourly wage.
hourly wage,
= 15900 / 73
= $217.8

So, Mr. Freeze gets paid of $217.8 hourly.

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Answer:

{9n+4z+96}{12}]

Step-by-step explanation:

Combine multiplied terms into a single fraction

{3}{4}n+(8+{1}{3}

{3n}{4}+(8+{1}{3}

Combine multiplied terms into a single fraction

{3n}{4}+(8+{1}{3}z)

{3n}{4}+( 8+{3}

Multiply by 1

{3n}{4}+8+3}

{3n}{4}+( 8+3}

Find common denominator

{3n}{4}+8+3}

3n}{4}+{3\8}{3}+3}

Combine fractions with common denominator

{3n}{4}+3\8}{3}+{3}

{3n}{4}+8+3}

Multiply the number

{3n}{4}+8}+z}{3}\right)

{3n}{4}+24}+z}{3}\right)

Rearrange terms

{3n}{4}+{24+z}}{3}

{3n}{4}+24}}{3}\right)

Find common denominator

\frac{3n}{4}+\frac{z+24}{3}

\frac{3\cdot 3n}{12}+\frac{4(z+24)}{12}

Combine fractions with common denominator

{3\ 3n}{12}+\{4(z+24)}{12}

{3\ 3n+4(z+24)}12

Multiply the numbers

{3}n+4(z+24)}{12}

{9}n+4(z+24)}{12}

Distribute

{4(z+24)}}{12}

{4z+96}}{12}

The percentage for blue balls will be 56% and the percentage for red balls will be 44%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage, therefore, refers to a component per hundred.

In this situation, there are 4000 balls and 2240 of then are blue while 1760 are red.

The percentage for blue balls will be:

= Number of blue balls / Total balls × 100

= 2240 / 4000 × 100

= 56%

The percentage for red balls will be:

= Number of red balls / Total balls × 100

= 1760 / 4000 × 100

= 44%

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The complete square of the a² + 2a - 3 = 0,a² - 2a - 8 = 0 and p² + 16p - 22 = 0 are (a + 1)² - 4 = 0,(a - 1)² - 9 = 0 and (p + 8)² - 86 = 0 respectively.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

As per the given trinomial,

a² + 2a - 3 = 0

a² + 2a = 3

Add 1 on both sides,

a² + 2a + 1 = 3 + 1

(a + 1)² = 4

(a + 1)² - 4 = 0

As per the given trinomial,

a² - 2a - 8 = 0

a² - 2a = 8

Add 1 on both sides,

a² - 2a + 1 = 8 + 1

(a - 1)² = 9

(a - 1)² - 9 = 0

As per the given trinomial,

p² + 16p - 22 = 0

p² + 16p = 22

Add 64 on both sides,

p² + 16p + 64 = 22 + 64

(p + 8)² = 86

(p + 8)² - 86 = 0

Hence "The complete square of the a² + 2a - 3 = 0,a² - 2a - 8 = 0 and p² + 16p - 22 = 0 are (a + 1)² - 4 = 0,(a - 1)² - 9 = 0 and (p + 8)² - 86 = 0 respectively".

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Answer:

  (300 ÷ 5) + (35 ÷ 5)

Step-by-step explanation:

You want an expression that has the same value as 335÷5.

The given division expression can be rewritten as ...

  [tex]335\div5=\dfrac{335}{5}\\\\=\dfrac{300+35}{5}=\dfrac{300}{5}+\dfrac{35}{5}\\\\=\boxed{(300\div5)+(35\div5)}[/tex]

Answer:

  (7)  (2, 4)

Step-by-step explanation:

You want to know which of the offered points is closest to the point of intersection of the two graphed lines.

The point of intersection can be read from the graph as approximately (2 1/3, 3 3/4). The nearest grid intersection to that point is (2, 4), which is the last point on the list of choices.

  (2, 4) is closest to the actual solution

__

Additional comment

You can see this, too, by graphing the offered choices. There are none closer than (2, 4).

The radius of the given cylinder is equal to r = 10 inches.

Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width, and height of the Cuboid.

For the cylinder, the formula for the volume will be,

V = πr²h

Given that the volume of the cylinder is 942 cubic inches. the radius of the cylinder base will be calculated as,

942 = π x ( r² ) x 12

r² = ( 942 x 4 ) / ( 12 x π)

r² = 100

r = 10 inch

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Answer:

c

Step-by-step explanation:

if u translate a line, there's not 2 lines?

To estimate the proportion of U.S adults who have no confidence at all in the media accurately reporting news, you can use the following steps:

Calculate the total number of adults surveyed by the Gallup organization. You can do this by adding the number of adults who said they had a great deal of confidence, a fair amount of confidence, not a lot of confidence, and no confidence at all:

Total number of adults = 81 + 325 + 397 + 214 = 1017

Calculate the proportion of adults who have no confidence at all by dividing the number of adults who said they had no confidence at all by the total number of adults:

Proportion of adults with no confidence = 214 / 1017

                                                                      = 0.2113

Therefore, the estimated proportion of U.S adults who have no confidence at all in the media accurately reporting news is approximately 0.2113, or 21.13%. This represents the proportion of adults who responded "no confidence at all" to the survey question.

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Answer:

Step-by-step explanation:

For 30: 1,2,3,5,6,10,15,30
For 21: 1,3,7,21
For 56: 1,2,4,7,8,14,28,56
Because you always go times it by the number. Example is: 1 is always in the factors (Doesn't matter if it's the least common factor or whatever) because whatever you times by 1, it's that answer. Or you can look at the answer, (I'm doing the 30) First, find the middle which is 5 and 6. You times 5 and 6 and it will give you 30. People call it a rainbow, 5x6=30, 3x10=30, 2x15=30, and 1x30=30.

I hope this  helps

Answer: k=4

Step-by-step explanation:

4x²-17x+k=0

Divide both parts of the equation by 4:

[tex]\displaystyle\\\frac{4x^2}{4}-\frac{17x}{4}+\frac{k}{4}=0\\\\x^2-\frac{17}{4} x +\frac{k}{4} =0\\[/tex]

Let one of the roots of this equation be α

Then the other root of this equation is 1/α

Hence,

[tex]\displaystyle\\\alpha (\frac{1}{\alpha })=\frac{k}{4} \\\\\frac{\alpha }{\alpha }= \frac{k}{4} \\\\1=\frac{k}{4}[/tex]

Multiply both parts of the equation by 4:

4=k

Thus, k=4

The required probability that a student selected at random will pass both French 101 and French 102 is 0.58.

Given that,
Class records at a particular college indicate that a student selected at random has a probability 0.67 of passing French 101. For the student who passes French 101, the probability is 0.88 that he or she will pass French 102.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
P(a) = 0.67 for passing French 101.
p(b) = 0.88 for passing French 102.
The probability that a student selected at random will pass both French 101 and French 102  = 0.67 × 0.88 = 0.58

Thus, the required probability that a student selected at random will pass both French 101 and French 102 is 0.58.

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The relation is a function in the first graph.

How to check which relation is function in given graph?

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