An engineering student is studying the effects of cryogenic treatments on a particular material. The treatment involves cooling the material with
specific applications of liquid nitrogen
The temperature of the material in degrees Celsius, y, can be modeled by the following graph, where x represents the time, in hours, since the
treatment began

The two smallest positive solutions, with a < b, are approximately

x ≈ 0.384 and x ≈ 1.64.

We have,

Isolate the sine function by dividing both sides by 8.

sin(5x) = 3/8

The inverse sine function (also called arcsin) is on both sides of the equation.

5x = arcsin(3/8).

Divide both sides by 5.

x = (1/5) arcsin(3/8)

Now,

arcsin(3/8) is approximately 0.4115.

So,

x = (1/5) * 0.4115

x = 0.384.

Since the sine function repeats itself every 2π radians, we add multiples of 2π/5 to the solution to find other valid values of x.

The second smallest positive solution

x = 0.384 + (2π/5) = 1.64.

Therefore,

The two smallest positive solutions, with a < b, are approximately

x ≈ 0.384 and x ≈ 1.64.

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The equation 8 sin(5x) = 3 is solved by isolating the variable term, using inverse sine to get an angle, and considering the period of the sine function when finding additional solutions.

To solve the equation 8 sin (5x) = 3, we first isolate the term involving the variable 'x'. Start by dividing both sides by 8. We get sin(5x) = 3/8.

The inverse sine (also known as arcsin or sin^-1) is used to get the angle whose sine is 3/8. So we have 5x = sin^-1(3/8).

To solve for 'x', we then divide both sides by 5: x = sin^-1(3/8) / 5.

This value of 'x' is a solution, but sine function repeats every 2π intervals, so we add multiples of 2π/5 to 'x' to get additional solutions.

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Answer:

20 %

Step-by-step explanation:

10000/200000

The percentage of the company she owns is equivalent to 5%.

In mathematics →

Given is that if Ruth contributed $10,000 toward the total group investment of $200,000 for the purchase of a seafood restaurant.

Assume that the percentage of the company she owns is equivalent to [x] percent. So, we can write -

10000 = [x]% 0f 200000

10000 = [x]/100 × 200000

10000 = [x] × 2000

[x] = (10000/2000)

[x] = 5%

Therefore, the percentage of the company she owns is equivalent to 5%.

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Answer: 76 child tickets were sold that day.

Step-by-step explanation:

You need to set up a system of equations.

Let be "c" the number of child tickets sold that Wednesday and "a" the number of adult tickets sold that Wednesday.

Then:

[tex]\left \{ {{a+c=173} \atop {9.40a+5.70c=1345.0}} \right.[/tex]

Using the Method of Elimination, you can multiply the first equation by -9.40, then add both equations and finally solve for "c":

[tex]\left \{ {{-9.40a-9.40c=-1626.2} \atop {9.40a+5.70=1345.0}} \right.\\..................................\\-3.7c=-281.2\\\\c=\frac{-281.2}{-3.7}\\\\c=76[/tex]

Answer:

20 centimeters

Step-by-step explanation:

27 / x = 12

x = 2.25 times

width would be 45 / 2.25 = 20 centimeters

Answer:

[tex]\dfrac{14}{75}[/tex]

Step-by-step explanation:

Gavin made 6 out of 15 shots, so the probability that Gavin's next shot will be  successful is

[tex]\dfrac{6}{15}=\dfrac{2}{5}[/tex]

Jack made 7 out of 15 shots, so the probability that Jack's next shot will be  successful is

[tex]\dfrac{7}{15}[/tex]

The probability that they both make their next shot successfully is

[tex]\dfrac{2}{5}\cdot \dfrac{7}{15}=\dfrac{14}{75}[/tex]

You must do pythagorean theorem:

a^2 + b^2 = c^2

a and b are the legs and c is the hypotenuse

In this triangle...

a = 16

b = x

c = 34

so...

16^2 + x^2 = 34^2

256 + x ^2 = 1156

x^2 = 900

Then to isolate x square root both sides. This will get rid of the square on the x value.

This will give you...

30

x is 30

Hope this helped!

Answer: second option

Step-by-step explanation:

You need to apply the Pythagorean theorem:

[tex]a^2=b^2+c^2[/tex]

Where "a"  is the hypotenuse and "b" and "c" are the legs of the right triangle.

In the figure you can observe the value the hypotenuse of the right triangle and the value of one of this leg. Then, you need to solve for the other leg from [tex]a^2=b^2+c^2[/tex]:

[tex]b^2=a^2-c^2[/tex]

[tex]b=\sqrt{a^2-c^2}[/tex]

Substituting values, you get that the value of "x" is:

 [tex]b=\sqrt{(34)^2-(16)^2}[/tex]

 [tex]b=30[/tex]

ANSWER

[tex]f(x) =x^3-6x^2-13x+42[/tex]

EXPLANATION

The zeros of the cubic function is given as:

x=7,x=-3,x=2

This implies that, x-7,x+3,x-2 are factors of the given cubic polynomial function.

We can write the completely factored form as a function of x to get:

[tex]f(x) = (x - 7)(x + 3)(x - 2)[/tex]

We expand to get:

[tex]f(x) = (x - 7)(x^2+ x-6)[/tex]

[tex]f(x) =x^3-6x^2-13x+42[/tex]

This is a cubic function because the highest degree is 3.

Answer:

fraction is 2/4

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

You could take these images (if you can visualize it)

And paste it into SM paint, and then reflect it.

But, if you look closely, A is just the notes higher, but not reflected, or changed in any other way.

C the second note is lower in the reflection. The notes shouldn't change in a reflection. Just the order.

ANSWER

B) 43

EXPLANATION

The given arithmetic sequence is 23, 28, 33, 38, . . .

We can observe the following pattern,

23+5=28

28+5=33

33+5=38

To obtain the subsequent terms, we add 5.

Therefore the next term is

38+5=43

Answer:

  D. 4 jump ropes, 3 people, 15 friends

Step-by-step explanation:

In order to answer the question how many friends could play, you need to be able to determine the smaller of ...

You can find the first of these numbers using the values of answer A, but if the number of Franklin's friends is smaller than 12, then you need to know that in order to properly answer the question. Hence, we believe you need to know ...

For this case we have that by definition, the surface area of a cone is given by:

[tex]SA = \pi * r * s + \pi * r ^ 2[/tex]

Where:

A: It's the radio

s: It's the slant

Substituting according to the data we have:

[tex]SA = \pi * 2.1 * 5.6 + \pi * (2.1) ^ 2\\SA = 36.9264 + 13.8474\\SA = 50.7738 \ m ^ 2[/tex]

If we round:

[tex]SA = 50.8 \ m ^ 2[/tex]

Answer:

True

Answer:

c. (3.75, 3.5)

Step-by-step explanation:

Let's call the given segment AB, and the dividing point P. Then you want AP:PB = 1:3.

There are a couple of ways you can get there.

1. Recognize that when you subtract the coordinates of A from P, the difference will be 1/4 of the result of subtracting A from B. That is, ...

P-A = (1/(1+3))·(B-A)

We can see that B-A = (6,8) -(3,2) = (3, 6), so 1/4 of that is (3/4, 3/2) = (0.75, 1.5). Adding these values to the coordinates of A gives ...

P = A + (.75, 1.5) = (3.75, 3.5)

__

2. Finish working out the equation above to solve for P:

4(P -A) = B -A

4P = B + 3A

P = (3A + B)/4 . . . . . note the multiplier for A is the relative length of PB and vice versa

P = (3(3, 2) +(6, 8))/4 = (15/4, 14/4) = (3.75, 3.5)

_____

Comment on choosing an answer

You only need to determine one of the coordinates in order to pick the correct answer. Finding both coordinates can help give you assurance that you have worked it out correctly.

Answer:

What do I love to do?

What brings me joy?

What am I naturally good at?

Answer is all of the above - last choice

Answer:

  Those line segments are parallel and all the same length.

Step-by-step explanation:

Translation modifies the coordinates of each point the same way, moving the point some distance in some direction. Hence the line segments connecting original to image points will all have the same length and direction.

_____

Comment on the question

The question is pretty open-ended. If it is multiple choice, perhaps there is a choice that more or less expresses the idea above. Otherwise, it is hard to tell what the question is driving at.

Answer:

california by 205.2

Step-by-step explanation:

3.8 times 107=406.6-California

1.9 times 106=201.4-Nebraska

205.2

Answer: The Population of California is larger than the population of Nebraska by 20 times

Step-by-step explanation:

Given

Population of California , [tex]P_C=3.8\times 10^{7}[/tex]

and population of Nebraska, [tex]P_N=1.9\times 10^{6}[/tex]

From above data it is clear that the population of California is larger than the population of Nebraska

And Ratio, [tex]\frac{P_C}{P_N}=\frac{3.8\times 10^{7}}{1.9\times 10^{6}}=\frac{38}{1.9}=20[/tex]

Thus the population of California is larger than the population of Nebraska by 20 times

Answer:

The minimun portion of inches that can be measured with the ruler is 1/16''.

Step-by-step explanation:

The precision , what is the minimun measurement that can be aprecciated by the ruler can be determined counting the number of disivion within 2 units.  To this ruler we can count 16 division bwtween one unit and asecutive one.

Answer:

c

Step-by-step explanation:

commission is basically 3 percent of what he sells he gets, sooooo 3 percent of 3800 is 114 (3800 × .03 because change the percent to decimal) and add it to his pay :)

Answer:

D

Step-by-step explanation:

Answer: He has 45.61

Step-by-step explanation:The answer is 45.61 because you add the decimals, 28.35+17.26, then you aline the decimal points and add, then get 45.61

1 1

28.35

+ 17.26

45.61

Total money John has now is 45.61.

On the first day of the month, John had $28.35 and received an additional $17.26.

To find out how much money John has now, you need to add the initial amount to the additional money he received. Therefore, John now has

28.35 + 17.26 = 45.61 money

Answer:

7,909 ft²

Step-by-step explanation:

If the diameter is 250 ft, that must mean the radius is 125 ft. For this problem, use the formula for area of a sector.

[tex]\frac{58}{360} \pi 125^{2}[/tex]

Answer:

≈ 7,909 ft^2

Step-by-step explanation:

The answer is:

The correct option is:

D) [tex](3^{2})^{6}=3^{12}[/tex]

To solve the problem, we need to remember the power of a power property, it's defined by the following way:

[tex](a^{m})^{n}=a^{m*n}[/tex]

When we have a power of a power, we must keep the base and then, the new exponent will be the product between the two original exponents.

So, we are given the expression:

[tex](3^{2})^{6}[/tex]

Then, calculating we have:

[tex](3^{2})^{6}=3^{2*6}=3^{12}[/tex]

Hence, we have that the correct option is:

D) [tex](3^{2})^{6}=3^{12}[/tex]

Answer:

The correct answer is option D).  3^12

Step-by-step explanation:

Points to remember

Identities

(xᵃ)ᵇ = xᵃᵇ

xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾

xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ⁾

It is given that (3^2)^6

To find the correct option

(3^2)^6 can be written as, (3²)⁶

By using above identities,  

(3²)⁶ = 3⁽² ˣ ⁶⁾

 = 3¹²

Therefore the correct answer is option D).  3^12

Answer:

Step-by-step explanation:

D=RT

10=1T

T=10 HOURS FOR THE TURTLE.

10=5(T-8)

10=5T-40

5T=10+40

5T=50

T=50/5

T=10 HOURS FOR THE RABBIT.

LOOKS LIKE A TIE .

The problem describes a situation with 16 girls who are four more than twice the number of boys. By setting up and solving the simple algebra equation 2x + 4 = 16, we find there are 6 boys in the club.

This is a word problem which can be solved using simple algebra. Given that there are 16 girls in the club and the number of girls is four more than twice the number of boys, we can set up the equation:

2x + 4 = 16

Where x stands for the number of boys. Solving this equation, we subtract 4 from both sides to get: 2x = 12. Dividing both sides by 2, we find that there are x = 6 boys in the club.

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Answer:

20.8%

Step-by-step explanation:

5/24= defective

^divide, and multiply by 100 to get percent

:)

The required percentage of defective parts is 20.8%.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,

After a group of 24 parts was tested. 5 were found defective.
The required percentage of the defective parts is given as,
= 5 / 24 × 100%
= 0.208 × 100%
= 20.8%

Thus, the required percentage of defective parts is 20.8%.

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Answer:

  33 ft

Step-by-step explanation:

The distance of interest is apparently not the straight-line distance from the top of the vertical ladder to the ground (20 ft), but the length of the arc the top of the ladder makes as it rotates. That arc length (s) is given by ...

  s = r·θ . . . . . where θ is the angle in radians subtended by the arc

Here, the radius is 20 ft, and the angle is the supplement of 85°, or 95° = (95/180)π radians.

  s ≈ (20 ft)·(1.65806 radians) ≈ 33.16 ft ≈ 33 ft

The answer to your question is B. 65

Answer:

b

Step-by-step explanation:

you add them all together and divide 11 because there are 11 numbers.

i used to have problem on mean, median, and mode too.

He can ask the student to raise their hands and pick them

the teacher can ask them to pick the closest number. the teacher can choose the students with the highest grades.

Answer:

1/7

Step-by-step explanation:

Answer:

i think it would be 1/7 also

Step-by-step explanation:

Answer:

Step-by-step explanation:

If we change those mixed fractions to improper we will have a much easier time with them:

[tex]\frac{\frac{10}{3} }{\frac{13}{5} }[/tex]

Now that looks horrible.  The rule for dividing fractions by fractions is a simple one, thankfully.  Bring the bottom fraction up next to the top fraction, then flip it upside down and change the sign to multiplication:

[tex]\frac{10}{3}[/tex]×[tex]\frac{5}{13}[/tex]

Multiply straight across the top and straight across the bottom to get

[tex]\frac{50}{39}[/tex]

Depending upon what your teacher calls "simplest form", this form may be the simplest, or the mixed fraction may be the simplest.  The mixed fraction equivalent to this improper is

[tex]1\frac{11}{39}[/tex]

Answer:

Step-by-step explanation:

First of all the answer.

[tex]\lim_{n \to -\infty}2^x= 1/ \lim_{n \to \infty}1/2^x = 0[/tex]

[tex]\lim_{n \to -\infty} 1-2^x = 1[/tex]

This approaches 0/1 = 0

The graph is included to show that this is the answer I get.