Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for metal sheets of a particular type, its mean value and standard deviation are 75 GPa and 1.7 GPa, respectively. Suppose the distribution is normal. (Round your answers to four decimal places.)

Required:
a. Calculate P(79 <= P <= 81) when n = 25.
b. How likely is it that the sample mean diameter exceeds 81 when n = 36?

Answer:

Step-by-step explanation:

3x - 5 = 0

3x = 5

x = 5/3

2x - 10 = 0

2x = 10

x = 10/2 = 5

9514 1404 393

Answer:

   0.0056

Step-by-step explanation:

  f(x) = √(49 +x)

  f'(x) = 1/(2√(49 +x))

A linear approximation of f(x) expanded about x=0 is ...

  f(x) ≈ f(0) + f'(0)x = 7 +x/(2·7)

Then for √53, we have x=4

  f(4) ≈ 7 +4/14 = 7 2/7 . . . . . approximate √53 using differentials

__

The calculator value of √53 is about 7.280110, so the difference in results is ...

  approx - actual ≈ 7.285714 -7.280110 = 0.005604 ≈ 0.0056

$5531.49

(9×9)×$68.29

Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine or tangent.

Remember: SOH-CAH-TOA

Looking from the given angle, we want to find the opposite side and we know the hypotenuse. Therefore, we should use sine.

sin(51) = BC / 58

BC = 58 x sin(51)

BC = 45.1 units

Hope this helps!

Step-by-step explanation:

Hey there!

From the above given figure;

Angle CAB = 51°

AB = 58

Taking Angle CAB as reference angle we get;

Perpendicular (p) = BC= ?

Hypotenuse (h) = 58

Now;

Taking the ratio of sin we get;

[tex] \sin( \alpha ) = \frac{p}{h} [/tex]

[tex] \sin(51) = \frac{bc}{58} [/tex]

Simplify it;

0.7771459*58 = BC

Therefore, BC = 45.0744.

Hope it helps!

Answer:

11 meters

Step-by-step explanation:

First, we can say that the square has a side length of x. The perimeter of the square is 4x, and that is how much wire goes into the square. To maximize the area, we should use all the wire possible, so the remaining wire goes into the triangle, or (11-4x).

The area of the square is x², and the area of an equilateral triangle with side length a is (√3/4)a². Next, 11-4x is equal to the perimeter of the triangle, and since it is equilateral, each side has (11-4x)/3 length. Plugging that in for a, we get the area of the equilateral triangle is

(√3/4)((11-4x)/3)²

= (√3/4)(11/3 - 4x/3)²

= (√3/4)(121/9  - 88x/9 + 16x²/9)

= (16√3/36)x² - (88√3/36)x + (121√3/36)

The total area is then

(16√3/36)x² - (88√3/36)x + (121√3/36) + x²

= (16√3/36 + 1)x² -  (88√3/36)x + (121√3/36)

Because the coefficient for x² is positive, the parabola would open up and the derivative of the parabola would be the local minimum. Therefore, to find the maximum area, we need to go to the absolute minimum/maximum points of x (x=0 or x=2.75)

When x=0, each side of the triangle is 11/3 meters long and its area is

(√3/4)a² ≈ 5.82

When x=2.75, each side of the square is 2.75 meters long and its area is

2.75² = 7.5625

Therefore, a maximum is reached when x=2.75, or the wire used for the square is 2.75 * 4 = 11 meters

The length of the square must be 4 m in order to maximize the total area.

When we put the differentiation of the given function as zero and find the value of the variable we get maxima and minima.

We have,

Length of the wire = 11 m

Let the length of the wire bent into a square = x.

The length of the wire bent into an equilateral triangle = (11 - x)

Now,

The perimeter of a square = 4 side

4 side = x

side = x/4

The perimeter of an equilateral triangle = 3 side

11 - x = 3 side

side = (11 - x)/3

Area of square = side²

Area of equilateral triangle = (√3/4) side²

Total area:

T = (x/4)² + √3/4 {(11 -x)/3}² _____(1)

Now,

To find the maximum we will differentiate (1)

dT/dx = 0

2x/4 + (√3/4) x 2(11 - x)/3 x -1 = 0

2x / 4 - (√3/4) x 2(11 - x)/3 = 0

2x/4 - (√3/6)(11 - x) = 0

2x / 4 = (√3/6)(11 - x)

√3x = 11 - x

√3x + x = 11

x (√3 + 1) = 11

x = 11 / (1.732 + 1)

x = 11/2.732

x = 4

Thus,

The length of the square must be 4 m in order to maximize the total area.

Learn more about maxima and minima here:

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Answer:

team a and team c scored 74 points which is 48 points more than team b, scoring 26 points.

Step-by-step explanation:

Answer: [tex]\dfrac{11}{9}I[/tex]

Step-by-step explanation:

Given

There is [tex]l[/tex] liter of pure alcohol

Suppose [tex]x[/tex] liters of water is added

After addition of water, alcohol becomes 45% in concentration

[tex]\Rightarrow \dfrac{l}{x+l}=45\%\\\\\Rightarrow \dfrac{I}{0.45}=x+I\\\\\Rightarrow \dfrac{20}{9}I-I=x\\\\\Rightarrow x=\dfrac{11}{9}I[/tex]

Thus,  [tex]\dfrac{11}{9}I[/tex] of water is added to the pure alcohol.

Answer:

x = 7

Explaination:

ABC = 40°

and BD bisects the angle so ABD = 20°

so 3x-1=20

solving for x gets us

x = 7

Given:

The equation is:

[tex]5x-2=4+2x[/tex]

To find:

The number that belongs in the green box and another box.

Solution:

We have,

[tex]5x-2=4+2x[/tex]

Subtracting 2x from both sides, we get

[tex]5x-2-2x=4+2x-2x[/tex]

[tex]3x-2=4[/tex]

Adding 2 on both sides, we get

[tex]3x-2+2=4+2[/tex]

[tex]3x=6[/tex]

We need to divide both sides by 3 to isolate the variable x.

On dividing both side by 3, we get

[tex]\dfrac{3x}{3}=\dfrac{6}{3}[/tex]

Therefore, the missing values are 3 and 3, and the required equation is [tex]\dfrac{3x}{3}=\dfrac{6}{3}[/tex].

Answer:

I think i don't know the answer i am so sorry!!!

maybe someone else can Answer

Answer:

Option B, 5/16

Step-by-step explanation:

f(4) = 5•(1/2)⁴

= 5•(1/2⁴)

= 5•(1/16)

= 5/16

The probability will be the same for both clocks.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

With one alarm clock, we have a 0.875 probability of being awakened.

The probability for the two clocks will be the same because both the clocks will ring at the same time.

To know more about probability follow

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Answer:

Easy, all you ha

Step-by-step explanation:

Answer:

a) 2.06

b) variance = 270.90 , std = 275.14

Step-by-step explanation:

a) Determine Expected rate of return

attached below is the calculated table for the solution provided

∴ Expected rate of return = ∑ Xp(x) = -6.46 + 3.84 + 4.68 = 2.06

b) Determine the variance and standard deviation

Variance ( Vx ) = E(x)^2 - [ Expected rate of return ]^2

                         = 275.14 - ( 2.06 )^2 ≈ 270.90

standard deviation = √ variance = √270.90 = 16.459

note : E(x)^2 = ∑ x^2 p(x) = 275.14

Answer:

16 days

Step-by-step explanation:

Here,

By the question,

4 men takes 4 days working each day 4 hours to complete 4 units of work..

then..

if 1 man works 1 hour each day then i would take ( 4×4×4 ) days

= 64days

then..

if 2 men work for 2 hours per day then.

it would take

4×4×4 / 2×2 days

= 16 days

Answer:

D

Step-by-step explanation:

8 and 3/5 = 8.2 and 8.2 is between 8 and 9 so the answer is D.

Answer:

y=2x+8

Step-by-step explanation:

Hope this helps

Answer:

Perfect complements

Step-by-step explanation:

Since minimum score of tests is to be considered. It is a case of perfect complements.

Correct option is

Perfect complements

In this question, we are given a matrix, and we have to perform the given operation.

The matrix is:

[tex]\left[\begin{array}{ccc}6&-1&|5\\1&-5&|0\end{array}\right][/tex]

The following operation is given:

[tex]R_1 \rightarrow -6R_2 + R_1[/tex]

In which [tex]R_1[/tex] is the element at the first line and [tex]R_2[/tex] is the element at the second line.

Updating the first line:

[tex]R_{1,1} = -6*1 + 6 = 0[/tex]

[tex]R_{1,2} = -6*-5 - 1 = 30 - 1 = 29[/tex]

[tex]R_{1,3} = -6*0 + 5 = 5[/tex]

Thus, the filled matrix will be given by:

[tex]\left[\begin{array}{ccc}0&29&|5\\1&-5&|0\end{array}\right][/tex]

For another example where row operations are applied on a matrix, you can check https://brainly.com/question/18546657

Answer:

2.8 litres

Step-by-step explanation:

8.22 mg per 3.039 mL

2.704 mg per 1 mL

7.469 gram = 7469 milligrams

7469 milligrams per 2,761.34927mL

= 2.761 litres = 2.8 litres

Answer:

Step-by-step explanation:

Short of taking 3 hours to type out the way that I did this, let me just tell you the process. Square both sides and multiply to distribute. You end up with radicals still, so square both sides again and multiply to distribute. What you end up with is a 6th degree polynomial that has to be factored. What I got in the end were these zeros:

x = 21.41917943

x = 1.306542114+/-7186864435i

x = -1.066667927

x = 1.28038353

x = 1.28038353

x = -.2459792634

Answer:

B. Yes. By SSS~

Step-by-step explanation:

From the diagram given, we have the corresponding sides of both triangles as follows:

RQ/KL = 24/20 = 6/5

QP/LM = 18/15 = 6/5

RP/KM = 12/10 = 6/5

From the above, we can see that the ratio of the corresponding side lengths of both triangles are equal. This means that all three sides of one triangle are proportional to all corresponding sides of the other triangle.

The SSS similarity theorem states that if all sides of one triangle are proportional to all corresponding sides of another, then both triangles are similar to each other.

Therefore, ∆KLM ~ ∆RQP by SSS similarity.

Answer:

8.6

Step-by-step explanation:

VW = WX / cos (36°)

= 7 / 0.81

= 8.6

Answer:

8.65

Step-by-step explanation:

cos 36° = 7 / VW

VW = 7 /  cos 36°

VW = 8.65

Hi there!

[tex]\large\boxed{\frac{1}{18}}[/tex]

1/3x = 6

Begin by multiplying both sides by 3 to cancel the fraction:

1/x = 18

Take the reciprocal of both sides:

x = 1/18

Answer:

1/18

Step-by-step explanation:

I N E E D P O I N T S :O)

Answer:

Step-by-step explanation:

First discount

90/100 * 90 = 81 dollars

Second discount.

Be careful. This is usually a discount from the price in part are.

5% of 81 = 5/100 * 81 = 4.05

81 - 4.05 = 76.95

Answer:

From the data The anxiety levels decreases as a result of the workshop

given that the mean value of the differences = -1.1125

Step-by-step explanation:

Number of randomly selected employees = 16

From the data It can be noticed that the difference in anxiety levels decrease ( Tends towards values below 0 )

To determine this we have to determine the mean value of the differences

(-3) + (-3) + (-2) +(-2) +(-2) + (-2 ) + (-1) + (-1) + (-1) + (-1) + (-1 ) + 0 + 0 + 0 + 0  + 1 / 16

= -18 / 16 = - 1.1125

mean value = -1.1125.

Answer:

There was enough evidence to reject the null hypothesis, and in fact, the null hypothesis is false, which means that no error was committed.

Step-by-step explanation:

A company specializing in parachute assembly claims that its main parachute failure rate is at most 1%.

At the null hypothesis, we test if the proportion is of at most 1%, that is:

[tex]H_0: p \leq 0.01[/tex]

At the alternative hypothesis, we test if the proportion is of more than 1%, that is:

[tex]H_0: p > 0.01[/tex]

Type I and type II errors:

Type I: Rejection of a true null hypothesis. The null hypothesis is true, but from a sample, you get enough evidence to reject.

Type II: Non-rejection of a false null hypothesis. The null hypothesis is false, but from a sample, you do not get enough evidence to reject.

Your sample data resulted in enough evidence to go against the claim made by the company.

This means that there was enough evidence to reject the null hypothesis.

It was later determined that the claim made by the company was actually incorrect.

The null hypothesis was false.

What kind of error, if any, was committed?

There was enough evidence to reject the null hypothesis, and in fact, the null hypothesis is false, which means that no error was committed.

Answer:

The Answer is K.

Step-by-step explanation:

K is the answer because it is the only other point on the line DK