Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms.
Find sin B and tan B.

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:

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:

1/7

Step-by-step explanation:

Answer:

i think it would be 1/7 also

Step-by-step explanation:

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 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:

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:

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:

A) 3x

Step-by-step explanation:

The total of all the volumes is ...

(x -1) + (x) + (x +1) = (1+1+1)x +(-1+1) = 3x+0 = 3x . . . . . matches choice A

Answer:

B

Step-by-step explanation:

If we imagine this is on a clock, then point P is at the 9-o'clock position.  When we rotate it 90 degrees clockwise, that's a quarter rotation, so P' will be at the 12-o'clock position.  So the coordinates of P' will be (0, 5).

Answer:

acceleration

Step-by-step explanation:

In a speed-time graph, the speed data is on the Y-axis and the time is represented on the X-axis.

A slope is the variation of Y-values over the variation of the X-values between to points.

So, the slope of a speed-time graph would be the variation of the speed over the variation of time.

Let's say your units are m/s for the speed and s for the time.

The slope units would then be calculated by dividing m/s by s... (m/s) / s....

That would give you m/s², which is an acceleration unit.

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:

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]

Answer:

The Experimental Probability of the spinner stopping on Section A is 1/3.

Step-by-step explanation:

Number of time spinner landed on section A = 4

Number of time spinner landed on section B = 5

Number of time spinner landed on section C = 2

Number of time spinner landed on section D = 1

Total Number of spins = 12

[tex]Probability=\frac{Number\:of\;Favorable\:outcome}{Number\:of\:total\;outcome}=\frac{4}{12}=\frac{1}{3}[/tex]

Therefore, The Experimental Probability of the spinner stopping on Section A is 1/3.

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:

360,000

Step-by-step explanation:

The exclamation point is factorial:

9! = 9×8×7×6×5×4×3×2×1 = 362880

5! = 5×4×3×2×1 = 120

4! = 4×3×2×1 = 24

362880 - 120× 24 = 360000

Answer:

i)

Find the attached

ii)

The mathematical model that best fits the data is;

y = 7.19 + 12.8 ln x

Step-by-step explanation:

i)

A scatter-plot can easily be constructed using applications such as Ms. Excel and Stat-Crunch.

In Ms. Excel we first enter the data in any two adjacent columns. Next, highlight the data, then click the insert ribbon and select the scatter-plot option.

Excel returns a scatter-plot chart as shown in the attachment below.

ii)

After obtaining the scatter-plot, we shall need to add a trend line in order to determine the mathematical model that best fits the data given.

Click anywhere inside the chart, then select the design tab under chart tools. Click on the Add Chart element in the upper left corner of the excel workbook and select more trend-line options. This feature will enable us to fit any trend-line to our data.

Select any trend line option ensuring you check the boxes; Display Equation on chart and Display R-squared value on chart.

Find the attached for the various trend-lines.

The mathematical model that best fits the data is;

y = 7.19 + 12.8 ln x

Since it has the largest R-squared value of 0.9905

[tex]\rm y = 7.19 + 12.8\ ln\ x[/tex], in this function, the scatter points follow this function. Then the correct option is C.

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

Construct a scatterplot and identify the mathematical model that best fits the data.

Assume that the model is to be used only for the scope of the given data and consider only linear, quadratic, logarithmic, exponential, and power models.

Use a calculator or computer to obtain the regression equation of the model that best fits the data.

You may need to fit several models and compare the values of R2.

A.  [tex]\rm y = 7.82x + 0.844[/tex], in this function, the scatter points do not follow this function.

B.  [tex]\rm y = 6.81 e^{0.316x}[/tex], in this function, the scatter points do not follow this function.

C.  [tex]\rm y = 7.19 + 12.8\ ln\ x[/tex], in this function, the scatter points follow this function. Because the best fits.

D.  [tex]\rm y = 4.40 + 5.00x[/tex], in this function, the scatter points do not follow this function.

The graph is shown.

More about the function link is given below.

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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 ...

Answer:

20 centimeters

Step-by-step explanation:

27 / x = 12

x = 2.25 times

width would be 45 / 2.25 = 20 centimeters

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:

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:

  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

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:

fraction is 2/4

Step-by-step explanation:

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.

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:

What do I love to do?

What brings me joy?

What am I naturally good at?

Answer is all of the above - last choice

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: 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]

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