A cylindrical 2014-t6 aluminum alloy bar is subjected to compression-tension stress cycling along its axis; results of these tests are shown in fig. 1. if the bar diameter is 12.0 mm, calculate the maximum allowable load amplitude (in newtons) to ensure that fatigue failure will not occur at 107 cycles.

Answer:

la respuesta es 86

Step-by-step explanation:

Answer:

The common difference is 1.5

Use the explicit formula to find a1.

a1 = 1.2

What is the explicit formula for the arithmetic sequence?

= 1.2 + (n - 1)1.5

Step-by-step explanation:

Final answer:

The common difference of the arithmetic sequence is 1.5, and the first term is 1.2. The explicit formula for the arithmetic sequence is A: an = 1.2 + (n - 1)1.5.

Explanation:

To find the common difference of an arithmetic sequence, we can use the information that the seventh term (a7) is 10.2 and the twelfth term (a12) is 17.7. The formula for the nth term of an arithmetic sequence is an = a1 + (n - 1)d, where a1 is the first term and d is the common difference. By creating a system of equations using the given terms, we can solve for d.

For the seventh term: 10.2 = a1 + 6d
For the twelfth term: 17.7 = a1 + 11d
Subtracting the first equation from the second gives: 17.7 - 10.2 = 5d, which simplifies to 7.5 = 5d or d = 1.5.

We can then plug the value of d back into one of the equations to find a1:
10.2 = a1 + 6(1.5)
10.2 = a1 + 9
a1 = 1.2

Therefore, the explicit formula for this arithmetic sequence is A: an = 1.2 + (n - 1)1.5.

There is a 1/36 or a ~2.8% chance that a player will roll two sixes. Because the dice is cubed, the player will have a 1/6 probability of rolling a six one time. Because the player needs to get six 2 times in a row, you would simply need to multiply 1/6 by itself twice(1/6•1/6 or 1/6^2) which equals 1/36.

Answer:

6(x + 3), or expanded: 6x + 18

Step-by-step explanation:

We start with x.

"Add 3" means + 3, so we have: x + 3

"Then times by 6" means multiply by 6, or * 6, so we have 6 * (x + 3)

Thus the expression is 6(x + 3), or expanded: 6x + 18

Hope this helps!

Answer:

6(x + 3)

Step-by-step explanation:

Add 3:

x + 3

Times 6:

6(x + 3)

The flight from NY to Chicago took roughly 2.12 hours, while the return flight took about 1.58 hours due to a tailwind. By using these times to calculate the speeds of the flights, we find that the tailwind was 113.04 mph.

The flight time from NY to Chicago can be calculated by dividing the distance (700 miles) by the speed of the plane (330 mph). The result is about 2.12 hours. The total flight time for the round trip is given as 3.7 hours, so the return trip took about 1.58 hours. Divide 700 miles by 1.58 hours and we get a total speed of about 443.04 mph for the return trip. This speed includes both the speed of the plane (330 mph) and the speed of the tailwind (x). Therefore, to find the speed of the tailwind, subtract the speed of the plane from the total speed: 443.04 mph - 330 mph = 113.04 mph. So, the tailwind is 113.04 mph.

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The tailwind speed is found to be approximately 113.04 mph.

Let's find out the time it takes for the initial flight from NY to Chicago.

Now, for the return trip, let the tailwind speed be denoted as x.

Let time for the return trip be t hours. Then, we have:

Therefore, the equation for the return trip will be:

Solving for x:

x ≈ 443.04 - 330 = 113.04 mph

The speed of the tailwind is approximately 113.04 mph.

Find the distance around the circle ( circumference)

Circumference = 2 x PI x r

Circumference = 2 x 3.14 x 200

Circumference = 1256 inches.

Divide circumference by spacing:

1256 / 4 = 314

You can plant 314 flowers.

Answer: 10×1.4^6

Step-by-step explanation:

This question is about exponential growth in mathematics.

This question is about exponential growth in mathematics. The number of people who received the email increases by a factor of 1.4 every week.

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Answer:

n = 10

Step-by-step explanation:

Solve for n:

(3 n)/5 = 6

Multiply both sides of (3 n)/5 = 6 by 5/3:

(5×3 n)/(3×5) = 5/3×6

5/3×3/5 = (5×3)/(3×5):

(5×3)/(3×5) n = 5/3×6

5/3×6 = (5×6)/3:

(5×3 n)/(3×5) = (5×6)/3

(5×3 n)/(3×5) = (3×5)/(3×5)×n = n:

n = (5×6)/3

6/3 = (3×2)/3 = 2:

n = 5×2

5×2 = 10:

Answer:  n = 10

To solve for n in 3⁄5 · n = 6, divide both sides of the equation by 3⁄5. The solution is n = 10.

To solve for n in the equation 3⁄5 · n = 6, we need to isolate n on one side of the equation. To do this, we can divide both sides of the equation by 3⁄5, which is the same as multiplying both sides by its reciprocal, 5⁄3. This cancels out the fraction on the left side, leaving us with n = 6 × 5⁄3. Multiplying 6 by 5 gives us 30, and dividing that by 3 gives us a final answer of n = 10.

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Answer:

The Answer is B

Step-by-step explanation:

Put the equation into desmos.com/matrix

it is a 2 row, 2 column matrix, hit Enter

Next line, press the letter A, then press the A^t button and it will give you the answer.

The transpose of matrix N is represented by b. [7  0  3 -2 ] , which correctly reflects the switching of rows and columns in the original matrix.

The correct answer is option B.

To find the transpose ([tex]N^t[/tex]) of a matrix N, we need to switch its rows and columns. Let's calculate the transpose of the given matrix N:

Matrix N:

```

N = [ 7   3 ]

     [ 0  -2 ]

```

Transpose of N ([tex]N^t[/tex]):

```

[tex]N^t[/tex]= [ 7  0 ]

         [ 3 -2 ]

```

So, the transpose of matrix N is:

```

[tex]N^t[/tex] = [ 7  0 ]

         [ 3 -2 ]

```

Now, let's compare the transpose we calculated with the options provided:

a. [ 0 -2   7 3 ] - This is not the transpose of N.

b. [7    0     3 -2 ] - This is the transpose of N.

c. [3   7    -2 0 ] - This is not the transpose of N.

d. [-2   3   0 7] - This is not the transpose of N.

So, the correct answer is option b:

```

[tex]N^t[/tex] = [7    0     3 -2 ]

```

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Answer:

A tiny but horrible alien is standing at the top of the Eiffel Tower (which is 324 meters tall) and threatening to destroy the city of Paris! A Men In Black agent is standing at ground level, 54 meters across the Eiffel square, aiming his laser gun at the alien. At what angle, in degrees, should the agent shoot his laser gun? Round your final answer to the nearest tenth

The agent shoot his laser gun at 80.5 degree.

Step-by-step explanation:

Given:

Height at which the horrible alien is standing = 324 m

Distance from the (tower) where the agent is = 54 m

According to the question:

Men In Black agent is aiming his laser gun to shoot the horrible alien.

Let the angle at which the agent shoot his gun be " Ф "

As from the situated depicted we can draw a right angled triangle.

Using trigonometric ratios:

tan (Ф) = opposite/ adjacent

In triangle OPQ .

The adjacent side = 54 m

The opposite side = 324 m

⇒ Plugging the values.

⇒ [tex]tan(\phi) = \frac{opposite}{hypotenuse}[/tex]

⇒  [tex]tan(\phi) = \frac{324}{54}[/tex]

⇒ [tex](\phi) = tan^-^1(\frac{324}{54})[/tex]

⇒ [tex]\phi=80.53[/tex]

Nearest tenth it is 80.5 degrees.

So,

Men In Black must shoot the laser gun at an angle of 80.5 degrees.

Final answer:

The Men In Black agent should shoot his laser gun at an approximate angle of 30.8 degrees to hit the alien at the top of the Eiffel Tower, after correcting the typos in the question.

Explanation:

To find the angle at which the Men In Black agent should aim his laser gun to hit the alien on top of the Eiffel Tower, we must solve a right triangle problem. The height of the Eiffel Tower is given as 324 meters, not 324324324 as stated in the question, which is likely a typo, and the horizontal distance (base of the triangle) from the agent to the base of the Eiffel Tower is 545 meters, not 545454 as stated, which seems to be another typo.

We use the tan inverse function (arctan) to calculate the angle. The angle θ is found using the formula:

θ = arctan(opposite/adjacent)

If h is the height of the tower and d is the distance across the ground, the angle θ equals:

θ = arctan(h/d)

Plugging in our values:

θ = arctan(324/545) ≈ arctan(0.5945)

Now we find the arctan of 0.5945 using a calculator:

θ ≈ 30.8 degrees

Therefore, the agent should shoot his laser gun at an angle of approximately 30.8 degrees.

Answer:

See below.

Step-by-step explanation:

PROBLEM A

The formula for the volume of a cylinder is

V = πr²h, where πr² is the area of the base.

V = area of base x height

*I will use the calculator button for pi (π)

Cylinder A: h = 1

10 = πr²h

10 = πr²(1)

10 = πr²                       Area of the base is 10m².

r = √ (10/π)

r = 1.78                        Radius is 1.78m.

d = 2r = 1.78*2 = 3.56                     Diameter is 3.56m.

Cylinder B: h = 2

10 = πr²h

10 = πr²(2)

5 = πr²                       Area of the base is 5m².

r = √ (5/π)

r = 1.26                      Radius is 1.26m.

d = 2r = 1.26*2 = 2.52                     Diameter is 2.52m.

Cylinder C: h = 4

10 = πr²h

10 = πr²(4)

2.5 = πr²                       Area of the base is 2.5m².

r = √ (2.5/π)

r = 0.89                        Radius is 0.89m.

d = 2r = 0.89*2 = 1.78                     Diameter is 1.78m.

Cylinder D: h = 5

10 = πr²h

10 = πr²(5)

2 = πr²                       Area of the base is 2m².

r = √ (2/π)

r = 0.80                     Radius is 0.8m.

d = 2r = 0.80*2 = 1.6                     Diameter is 1.6m.

The answers are reasonable if the answer is close to 10 when you substitute the rounded numbers back into the formula and solve.

There are infinite possibilities because any numbers when used in the formula equates to 10 are possible. The height/radius can be any decimal number, which would make the other dimensions change.

PROBLEM B

Follow similar steps if you know the diameter of a cylinder. Use the same formula V = πr²h.

We need the radius, which is half the diameter. r = d/2 = 10/2 = 5

Cylinder A: V = 100

100 = π25h

4 = πh

h = 1.27                      The height is 1.27m.

Cylinder B: V = 200

200 = π25h

8 = πh

h = 2.55                      The height is 2.55m.

Cylinder C: V = 75

75 = π25h

3 = πh

h = 0.95                      The height is 0.95m.

Cylinder D: V = 125

125 = π25h

5 = πh

h = 1.59                      The height is 1.59m.

The answers are reasonable if I can substitute two rounded values into the formula and get a number close to the third. The height is also a decimal number which occurs because of pi.

Given:

Given that the first term of the geometric sequence is 729.

The common ratio is [tex]\frac{1}{3}[/tex]

We need to determine the seventh term of the sequence.

Seventh term:

The seventh term of the sequence can be determined using the formula,

[tex]a_n=a_1(r)^{n-1}[/tex]

To find the seventh term, let us substitute n = 7 in the above formula, we get;

[tex]a_7=a_1(r)^{6}[/tex]

Now, substituting [tex]a_1= 729[/tex] and [tex]r=\frac{1}{3}[/tex], we get;

[tex]a_7=729(\frac{1}{3})^{6}[/tex]

[tex]a_7=729(\frac{1}{729})[/tex]

[tex]a_7=1[/tex]

Thus, the seventh term of the geometric sequence is 1.

Answer:

p= 9(6)+3(-4)

p= 42

hope this help

Answer:

42

Step-by-step explanation:

P=9r+3q

When q equals to a negative 4 and when r is aswell the number 6.It means to substitute

P=9(6)+3(-4)

p=54-12

p=42

Answer:

  39 miles

Step-by-step explanation:

The given distances are at right angles to each other, so form the legs of a right triangle whose hypotenuse is the straight-line distance of interest. The Pythagorean theorem can be used to find the length of the hypotenuse.

__

Your familiarity with Pythagorean triples lets you recognize the ratio of the distances, 15/36 = 5/12, means the triangle of interest is a multiple of the (5, 12, 13) Pythagorean triple. The multiplier is 3, so ...

  the direct distance to her aunt's house is 39 miles.

__

Additional comment

The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the other two sides:

  c² = a² +b²

  c = √(15² +36²) = √1521 = 39 . . . . hypotenuse for legs 15 and 36

__

Some Pythagorean triples you will run across in algebra, geometry, and trig problems are ...

  (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17), (9, 40, 41)

As here, you will also see multiples of these.

Answer:

x=1

Step-by-step explanation:

Given:

Given that the graph of the line.

We need to determine the equation of the line.

Slope:

The slope of the line can be determined using the formula,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Let us substitute any two points that the line passes through.

Substituting the point (3,0) and (0,-2) in the formula, we get;

[tex]m=\frac{-2-0}{0-3}[/tex]

[tex]m=\frac{-2}{-3}[/tex]

[tex]m=\frac{2}{3}[/tex]

Thus, the slope of the equation is [tex]m=\frac{2}{3}[/tex]

y - intercept:

The y - intercept of the equation is the point at which the line passes through the y - axis.

Thus, from the graph, the value of y - intercept is b = -2.

Equation of the line:

The equation of the line can be determined using the formula,

[tex]y = mx+b[/tex]

Substituting the values, we have;

[tex]y=\frac{2}{3}x-2[/tex]

Taking LCM, we have;

[tex]y=\frac{2x-6}{3}[/tex]

Multiplying both sides by 3, we get;

[tex]3y=2x-6[/tex]

Subtracting both sides by 2x, we get;

[tex]3y-2x=-6[/tex]

Thus, the equation of the line is [tex]3y-2x=-6[/tex]

Hence, Option 2 is the correct answer.

Answer:

The fraction of the applicants who have passed the two phases of the selection process is [tex]\frac{10}{63}[/tex].

Step-by-step explanation:

The question is:

In the first phase of the selection process for the body of teachers they eliminate four-ninth of the applicants while in the second phase they eliminate 5/7 of those who passed the first phase. If there were 315 applicants what is the fraction of the applicants who have passed the two phases of the selection process?

The total number of applicants is

N = 315.

It is provided that 4/9th of the applicants were eliminated in the first phase.

Then the fraction of candidates who passed the first phase is:

Fraction who passed phase I = [tex]1-\frac{4}{9}=\frac{5}{9}[/tex]

Now, it is also provided that 5/7 of those who passed the first phase were eliminated in the second phase.

Then the fraction of candidates who passed the second phase is:

Fraction who passed phase II = [tex]1-\frac{5}{7}=\frac{2}{7}[/tex]

That is, 2/7 of the remaining applicants passed the second phase.

The fraction of the applicants who have passed the two phases is:

[tex]\frac{5}{9}\times \frac{2}{7}=\frac{10}{63}[/tex]

Thus, the fraction of the applicants who have passed the two phases of the selection process is [tex]\frac{10}{63}[/tex].

Answer:

Therefore required expression is

y =462 - t×15

where y represents the amount of money in her bank account in dollar after t week.

Step-by-step explanation:

Given that,

Holly has $462 in her bank account and takes out $15 each week but does not put any back in.

She takes out $15 on first week.

The remaining amount of her bank account is =$(462-15)

                                                                            =$(462 - 1×15)

If she withdraws $15 on second week.

The remaining amount of her bank account is =$(462-15-15)

                                                                            =$(462 - 2×15)

Similarly after third the amount in her account is =$(462 - 3×15)

From the above it is cleared that

The amount in her account after t week is

=$(462 - t×15)

Therefore required expression is

y =462 - t×15

where y represents the amount of money in her bank account in dollar after t week.

Answer:

5/33

Step-by-step explanation:

5/12 * 4/11 = 20 /132 = 10 / 66 = 5 / 33

The probability of drawing a red marble on the first try is 5/12 because there are 5 red marbles and 12 marbles in total. The second time you only have 4 red marbles left and 11 marbles left in total. Multiply them to find the probability of drawing 2 red marbles in a row.

Probability of drawing 2 red marble is [tex]\frac{5}{33}[/tex]

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Here,

Number of red marbles = 5 marble

Number of green marbles = 7 marble

Probability =  Number of favorable outcome / Number of total outcome

Probability of drawing 1 red marble = [tex]\frac{5}{12}[/tex]

Probability of drawing second marble is red = [tex]\frac{4}{11}[/tex]

Probability of drawing 2 red marbles = [tex](\frac{5}{12})(\frac{4}{11} )=\frac{5}{33}[/tex]

Hence, the probability of drawing 2 red marble is [tex]\frac{5}{33}[/tex]

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Answer:

B. 80.2

Step-by-step explanation:

The easiest way to find the area of this figure is to divide it into two rectangles.

First, let's find the area of the top rectangle.

10.2 * 3 = 30.6

The area of the top rectangle is 30.6 square in.

Now let's find the area of the second rectangle:

6.2 * 8 = 49.6

The area of the bottom rectangle is 49.6 square in.

Lastly, we have to add the areas of the two rectangles together.

30.6 + 49.6 = 80.2

The area of the entire figure is 80.2 square inches.

Answer:

your 2 numbers are going to be 7 and 22

Answer:

50

Step-by-step explanation:

The measure of AU is 50.

An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc.

Given:

arc QU = 88 and <QUA = 111

QDA = 2 <QUA

         = 2 X 111

         = 222

Now, QUA = 360- 222 = 138

arc AU = QUA - arc QU

            = 138- 58

            = 50

Hence, the measure of AU is 50.

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Answer:

Power

Step-by-step explanation:

Term Definition

power: Measure of the amount of work that can be done in a given amount of time.

Answer:

Power

Step-by-step explanation:

power, measure of the amount of work that can be done in a given amount of time.

I hope this helps :)

Answer:

do 35 divided by 15 then just put that into fraction form

Step-by-step explanation:

Answer:

two fifths is the answer because you would divide 15 by 35 to get .4 which is two fifths.

Answer:

A = 80 m^2

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh  where b is the base length and h is the height

A = 1/2 (16) *10

A = 80 m^2

Answer:

A = 80

Step-by-step explanation:

A = .5bh

A = .5(16)(10)

A = 80

Can I get brainliest

Answer:

1/6 or 1.666667

Step-by-step explanation:

(y2-y1)/(x2-x1)

(15-10)/(21- -9) = 1/6

Answer:

1/6

Step-by-step explanation:

Answer:

Step-by-step explanation:

Confidence interval is written as

Sample mean ± margin of error

Margin of error = z × population standard deviation/sample size

A higher confidence level gives a higher z score. Reducing z and increasing number of samples could reduce the margin of error.

To reduce the margin of error, the correct options are

A) They could construct the confidence interval with a lower confidence level than they previously used.

B) They could include a greater number of subjects in the experiment.

Answer: 32%

Step-by-step explanation:

The total number of students that signed up for chemistry and algebra

two is 386.

Let x represent the number of students that signed up for both chemistry and algebra two

If 209 students signed up for algebra two, then the number of students that signed up for algebra two only is

209 - x

If 300 need to have signed up for chemistry, then the number of students that need to have signed up for chemistry only is 300 - x

Therefore,

x + 209 - x + 300 - x = 386

- x + 509 = 386

x = 509 - 386

x = 123

If 123 students would be signed up for both courses, then the probability that a student chosen at random from the 386 will be signed up for both of the courses is

123/386 × 100 = 32%

Answer: The number was 9.

Step-by-step explanation:

Let the number be 'x;.

think of a number, multiply it by five and subtract three from the result :

According to Ashton, the expression would be :

[tex]5x-3[/tex]

Kamir tells Andrew to think of a number, add five and multiply the result by three:

According to Kamir, the expression would be :

[tex]3(x+5)[/tex]

At last, they get the same number :

[tex]5x-3=3(x+5)\\\\5x-3=3x+15\\\\5x-3x=15+3\\\\2x=18\\\\x=\dfrac{18}{2}\\\\x=9[/tex]

Hence, the number was 9.

By comparing Ashton's algebraic expression '5x-3' with Kamir's expression '3(x+5)', one can find that if these expressions are equal, the number x that Andrew was thinking of is 15.

The subject of this question is Mathematics and it is suitable for a Middle School grade level. The trick that Ashton and Kamir are trying to figure out is based on one of the basic properties of numbers. Andrew says that regardless of the trick, he gets the same answer. This implies that the operations used in both tricks must have equivalent results. Let's use algebraic expressions to represent the steps in each trick. If the original number Andrew thinks of is x:

According to Andrew, these expressions are equal. So, we have the equation:

5x - 3 = 3(x + 5)

By solving this equation, you can find the original number that Andrew was thinking about, which is 15.

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Answer:

The inference is valid.

Step-by-step explanation:

In this case we need to test whether, 80% of students who had an opinion agree that school library hours should be extended.

A sample of 120 students were selected.

Of these 120, 50 students had an opinion and 70 did not.

Since we need to test for the students having an opinion, the sample size is, n = 50.

The sample proportion of students who had an opinion and agreed is:

[tex]\hat p=\frac{40}{50}=0.80[/tex]

The hypothesis can be defined as follows:

H₀: The proportion of students who had an opinion agree that school library hours should be extended is 80%, i.e. p = 0.80.

Hₐ: The proportion of students who had an opinion agree that school library hours should be extended is different from 80%, i.e. p ≠ 0.80.

The z-test for single proportion will be used.

The test statistic is:

[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.80-0.80}{\sqrt{\frac{0.80(1-0.80}{50}}}=0[/tex]

The test statistic value is 0.

Compute the p-value of the test:

[tex]p-value=2\times P (Z < 0)\\=2\times 0.50\\=1[/tex]

The p-value of the test is 1.

The p-value is very large, so the null hypothesis will not be rejected at any significance level.

Thus, it can be concluded that the proportion of students who had an opinion agree that school library hours should be extended is 80%.

Hence, the inference is valid.